hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Category of representations
In representation theory, the category of representations of some algebraic structure A has the representations of A as objects and equivariant maps as morphisms between them. One of the basic thrusts of representation theory is to understand the conditions under which this category is semisimple; i.e., whether an object decomposes into simple objects (see Maschke's theorem for the case of finite groups).

The Tannakian formalism gives conditions under which a group G may be recovered from the category of representations of it together with the forgetful functor to the category of vector spaces.

The Grothendieck ring of the category of finite-dimensional representations of a group G is called the representation ring of G.

Category of modules
In algebra, given a ring , the category of left modules over  is the category whose objects are all left modules over  and whose morphisms are all module homomorphisms between left -modules. For example, when  is the ring of integers , it is the same thing as the category of abelian groups. The category of right modules is defined in a similar way.

One can also define the category of bimodules over a ring  but that category is equivalent to the category of left (or right) modules over the enveloping algebra of  (or over the opposite of that).

Note: Some authors use the term module category for the category of modules. This term can be ambiguous since it could also refer to a category with a monoidal-category action.
François-Henri Pinault
François-Henri Pinault (French: [fʁɑ̃swa ɑ̃ʁi pino]; born 28 May 1962) is a French businessman and the son of billionaire François Pinault. François-Henri took the reins of his father's retail conglomerate Pinault-Printemps-Redoute in 2005, and turned it into the luxury group Kering (Gucci, Yves Saint Laurent, Balenciaga, Bottega Veneta) in 2013. He has been president of the family-owned investment holding Groupe Artémis (Château Latour, Christie's, Pinault Collection, Creative Artists Agency) since 2003. He has been married to the film producer and actress Salma Hayek since 2009.

Kering
Kering S.A. (French: [kɛːʁiŋ]) is a French multinational holding company specializing in luxury goods, headquartered in Paris. It owns the brands Gucci, Yves Saint Laurent, Balenciaga, Bottega Veneta, Creed, Maui Jim, and Alexander McQueen, among others.

The timber-trading company Pinault S.A. was founded in 1962, by François Pinault. After the company was quoted on Euronext Paris in 1988, it became the retail conglomerate Pinault-Printemps-Redoute (PPR) in 1994. The luxury group was rebranded Kering in 2013. It has been a constituent of the CAC 40 since 1995. François-Henri Pinault has been President of Kering since 2005, and Luca de Meo CEO since September 2025. In 2024, the group's revenue reached €17.2 billion.
Buckland, Massachusetts
Buckland is a town in Franklin County, Massachusetts, United States. The population was 1,816 at the 2020 census. The town shares the village of Shelburne Falls with neighboring Shelburne.  The town center at Shelburne Falls is the western end of the Bridge of Flowers, a local tourist attraction.

Buckland is part of the Springfield, Massachusetts Metropolitan Statistical Area.

Shelburne Falls, Massachusetts
Shelburne Falls is a historic village in the towns of Shelburne and Buckland in Franklin County, Massachusetts, United States. The village is a census-designated place (CDP) with a population of 1,731 at the 2010 census. It is part of the Springfield, Massachusetts, Metropolitan Statistical Area.
Matteo I Visconti
Matteo I Visconti (1250 – 24 June 1322) was the second of the Milanese Visconti family to govern Milan. Matteo was born to Teobaldo Visconti and Anastasia Pirovano.

In 1287, Matteo's uncle Ottone Visconti, archbishop and first lord of Milan, nominated him as capitano del popolo of Milan. Following his uncle's death in 1295, he succeeded him as lord of Milan. Matteo was appointed numerous times as Imperial Vicar over the whole of Lombardy, while expanding, with the assistance of his sons, his sphere of influence to Piedmont, Emilia, Bologna, and Genoa. Caught between the Papal and Imperial power struggle over northern Italy, Matteo would renounce his imperial title as "General Lord of the Milanese People". Found guilty on the charge of necromancy, excommunicated, and facing a crusade, Matteo resigned his position and died months later. He was succeeded by his son Galeazzo I.

Ottone Visconti
Ottone Visconti (1207 – 8 August 1295) was Archbishop of Milan and Lord of Milan, the first of the Visconti line. Under his rule, the commune of Milan became a strong Ghibelline city and one of the Holy Roman Empire's seats in Italy.
Essex 2
Essex 2 (also known as Essex Spitfire 2 for sponsorship reasons) was an English Rugby Union league at the tenth tier of the domestic competition. It was the basement division of club rugby in Essex with promoted teams moving up to Essex 1 and no relegation (up until 2008-09 relegated teams dropped to Essex 3 but this division has since been abolished). Essex 2 was created in 2003 by Essex-based teams who left East Counties 3 South. At the end of the 2013–14 season the division was abolished with teams either moving up into Essex 1 or into various Essex Merit leagues.

Eastern Counties 3
Eastern Counties 3 is an English level 11 Rugby Union league, currently divided into 3 regional leagues (north, south, west). Promoted teams moved up to the relevant regional divisions in Eastern Counties 2 while since the abolition of Eastern Counties 4 at the end of the 2016–17 season there has been no relegation. For most of its history, Eastern Counties 3 was divided into two regional divisions – north and south – with teams from Cambridgeshire, Norfolk, Suffolk and Essex taking part. A breakaway of Essex teams at the end of the 2002–03 to form a new league would lead to Eastern Counties 3 being abolished by the end of 2003–04 only to return due to a league restructure to cater for more 2nd and 3rd teams.
Rivière Noire Sud-Ouest
The Rivière Noire Sud-Ouest (Black River Southwest) is a tributary of the south shore of the Noire River flowing, entirely in the unorganized territory from Mont-Élie in Charlevoix-Est Regional County Municipality, in Quebec, Canada.

The lower part of this valley is served by route 170 which links Saint-Siméon to Petit-Saguenay, which passes on the north shore of the Noire River. This valley has some secondary forest roads for forestry and recreational tourism purposes.

Forestry is the first economic activity in the sector; recreational tourism activities, second.

The surface of "rivière Noire Sud-Ouest" is usually frozen from the beginning of December to the end of March, however, safe ice circulation is generally from mid-December to mid-March.

Noire River (Charlevoix)
The Noire River is a tributary of the North-West shore of Saint Lawrence River flowing north-east of La Malbaie, in  the municipality of Saint-Siméon, in Charlevoix-Est Regional County Municipality, in Quebec, in Canada.

The lower portion of this valley is served by Route 138 which runs along the shoreline of the St. Lawrence River. Route 170 which links Saint-Siméon to Petit-Saguenay village serves the lower and middle parts of this valley. The upper part of the valley has some secondary forest roads for forestry and recreation purposes.

Forestry is the first economic activity in the sector; recreational tourism activities, second.

The surface of the Black River is usually frozen from early December to late March, however, safe ice movement is generally from mid-December to mid-March.
Extremal length
In the mathematical theory of conformal and quasiconformal mappings, the extremal length of a collection of curves  is a measure of the size of  that is invariant under conformal mappings. More specifically, suppose that  is an open set in the complex plane and  is a collection
of paths in  and  is a conformal mapping. Then the extremal length of  is equal to the extremal length of the image of  under . One also works with the conformal modulus of , the reciprocal of the extremal length.  The fact that extremal length and conformal modulus are conformal invariants of  makes them useful tools in the study of conformal and quasi-conformal mappings. One also works with extremal length in dimensions greater than two and certain other metric spaces, but the following deals primarily with the two dimensional setting.

Quasiconformal mapping
In mathematical complex analysis, a quasiconformal mapping is a (weakly differentiable) homeomorphism between plane domains which to first order takes small circles to small ellipses of bounded eccentricity. Quasiconformal mappings are a generalization of conformal mappings that permit the bounded distortion of angles locally. Quasiconformal mappings were introduced by Grötzsch (1928) and named by Ahlfors (1935),

Intuitively, let f : D → D′ be an orientation-preserving homeomorphism between open sets in the plane. If f is continuously differentiable, it is K-quasiconformal if, at every point, its derivative maps circles to ellipses with the ratio of the major to minor axis bounded by K.
Ballastless track
A ballastless track or slab track is a type of railway track infrastructure in which the traditional elastic combination of sleepers and ballast is replaced by a rigid construction of concrete or asphalt. It is considered the standard for high-speed and heavy-haul railway lines. It is also commonly used for urban tramways.

Railway track
Railway track (CwthE and UIC terminology) or railroad track (NAmE), also known as permanent way (per way) (CwthE) or "P way" (BrE and Indian English), is the structure on a railway or railroad consisting of the rails, fasteners, sleepers (railroad ties in American English) and ballast (or slab track), plus the underlying subgrade. It enables trains to move by providing a dependable, low-friction surface on which steel wheels can roll. Early tracks were constructed with wooden or cast-iron rails, and wooden or stone sleepers. Since the 1870s, rails have almost universally been made from steel.
Scottish Football Federation
The  Scottish Football Federation was an association football competition formed in 1891 which ran for just two seasons.  The proposal for a competition came from seven clubs (Falkirk, King's Park, Royal Albert, Glasgow Wanderers, Pollokshaws, Kilmarnock Athletic, and Arthurlie) which had been overlooked for the Scottish League and Scottish Football Alliance.

In 1893 it was absorbed by the Scottish Football Alliance when that league lost all but one of its members to the Scottish Football League's new Division Two.

Scottish Football Alliance
The Scottish Football Alliance was a league football structure set up in Scotland in competition with the Scottish Football League. Its success in the early years of professional football in both England and Scotland made the Alliance the basis for a second division in both countries. The Alliance attracted a number of Junior clubs to the League system, which boosted its future viability.
Uneapa language
Uneapa (often called "Bali", natively Uniapa) is an Oceanic language spoken by about 10,000 people on the small island of Bali (Uneapa), north of West New Britain in Papua New Guinea. It is perhaps a dialect of neighboring Vitu. Uneapa is one of the most conservative Oceanic languages, having retained most of Proto-Oceanic's final consonants with an echo vowel, such as *Rumaq 'house' > rumaka and *saqat 'bad' > zaɣata.

A sketch grammar of this language was published in 2002 by Malcolm Ross.

Vitu language
Vitu (also spelled Witu or Vittu, referred by their own speakers as pole matotota 'true speech' or pole Vitu 'Vitu speech') or Muduapa is an Oceanic language spoken by about 7,000 people on the islands northwest of the coast of West New Britain in Papua New Guinea.
Robsonius
Robsonius is a genus of passerine birds in the family Locustellidae endemic to the Philippines.  The genus was introduced by the English ornithologist Nigel J. Collar in 2006 with the Cordillera ground warbler (Robsonius rabori) as the type species. The name was chosen to honour the British ornithologist Craig R. Robson.

The genus contains the following species:

Cordillera ground warbler (Robsonius rabori)

Sierra Madre ground warbler (Robsonius thompsoni)

Bicol ground warbler (Robsonius sorsogonensis)

Cordillera ground warbler
The Cordillera ground warbler (Robsonius rabori), also known as Rabor's wren-babbler or the Luzon wren-babbler, is a species of bird currently placed in the family Locustellidae.  It is endemic to the Philippines, where it is found in northwest Luzon in the foothills of the Cordillera Mountain Range.s natural habitat is tropical moist lowland forests. It was formerly conspecific and forms a species complex with the Bicol ground warbler and Sierra Madre ground warbler,  which are some of most elusive birds in the country due to their extremely shy nature. Among these three elusive species, the Cordillera ground warbler is the rarest and most threatened. It has only been photographed once in the wild. It is threatened by habitat loss.
The Conmen in Vegas
The Conmen in Vegas is a 1999 Hong Kong action comedy film produced, written and directed by Wong Jing and is a sequel to the 1998 film The Conman. The film stars original returning cast members Andy Lau and Nick Cheung with new cast members Natalis Chan, Kelly Lin, Meggie Yu, Alex Man and Jewel Lee in her debut film role. The film was partially filmed in the Caesars Palace Resort, Las Vegas.

The Conman
The Conman is a 1998 Hong Kong action comedy film directed by Wong Jing and starring Andy Lau, Athena Chu and Nick Cheung. Despite the Chinese title, which translates as Knight of Gamblers 1999, Andy Lau does not reprise his role as the "Knight of Gamblers" from the God of Gamblers series, which was also directed by Wong Jing. The film was followed by a sequel, The Conmen in Vegas, in which Lau and Cheung return with new cast members Natalis Chan, Kelly Lin, Meggie Yu and Alex Man.
Gille Brigte of Galloway
Gille Brigte or Gilla Brigte mac Fergusa of Galloway (Galloway, 1126 - 1185), also known as Gillebrigte, Gille Brighde, Gilbridge, Gilbride, etc., and most famously known in French sources as Gilbert, was Lord of Galloway of Scotland (from 1161 with Uchtred; 1174 alone, to 1185). Gilla Brigte was one of two sons of the great Fergus, the builder of the "Kingdom" of Galloway.

Uhtred of Galloway
Uhtred mac Fergus (c. 1120 – 22 September 1174) was Lord of Galloway from 1161 to 1174, ruling jointly with his brother Gille Brigte (Gilbert). They were sons of Fergus of Galloway; it was believed that they were half brothers, but Duncan of Carrick was addressed as cousin by the English King, as was Uchtred. (The term "cousin" in address does not necessarily connote a family tie; it was used between even minor "kings" to suggest that sender and receiver were of mutually considerable rank). Their mother's name is not known for sure, but she must have been one of the many illegitimate daughters of Henry I of England, most likely Elizabeth Fitzroy.
Brazilian Resolution
The Brazilian resolution was presented to the Economic and Social Council of the United Nations in 2003.
The resolution covered human rights and sexual orientation. It came under the Commission on Human Rights, fifty-ninth session, item 17 on the agenda.

Discussion of the resolution was postponed in 2004 because it was felt that it would not be passed.  A formal UN declaration on sexual orientation and gender identity was discussed in the General Assembly on 18 December 2008.

LGBTQI+ rights at the United Nations
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Discussions of LGBTQI+ rights at the United Nations have included resolutions and joint statements in the United Nations General Assembly and the United Nations Human Rights Council (UNHRC), attention to the expert-led human rights mechanisms (such as the United Nations Treaty Bodies and Special Procedures), as well as by the UN Agencies.

As of 2025, same-sex marriage is legally performed and recognized in 38 UN member states.
De Havilland Australia
de Havilland Aircraft Pty Ltd (DHA) was an Australian subsidiary of the British aircraft manufacturer de Havilland, founded in 1927. It acquired the Commonwealth Aircraft Corporation in 1985 and was purchased by Boeing in 2000 and merged with the Boeing owned AeroSpace Technologies of Australia (formerly Government Aircraft Factories) to become Hawker de Havilland Aerospace Pty Ltd. In 2009, the name was changed to Boeing Aerostructures Australia and is a subsidiary of Boeing Australia.

Boeing Australia
Boeing Australia is Boeing's largest subdivision outside the United States. Established in 1997, the company oversees its seven wholly owned subsidiaries, consolidating and co-ordinating Boeing's businesses and operations in Australia.

Boeing has played a role in Australia's aerospace industry through its products and services and has more than 4,500 employees spread across 38 locations in every state and territory except Tasmania. With an investment of more than $800 million, Boeing generates approximately $400 million in export revenue for Australia through its commercial and defence products and services.
Michipicoten River
The Michipicoten River (/mɪtʃɪpɪˈkɒtən/) is a river in Algoma District of northern Ontario, Canada, which flows from Dog Lake and joins with the Magpie River to empty into Michipicoten Bay on Lake Superior near the town of Wawa. This river is 113 km (70 mi) in length (including Lochalsh River to the outlet of Wabatongushi Lake) and drains an area of about 5,200 km2 (2,000 sq mi).

The river's name derives from the Ojibwe Mishipikwadina, meaning "big bluffs," and refers to the large hills located near the river's mouth.

From the outlet of Dog Lake, the Michipicoten River flows south through a series of large lakes: Manitowik and Whitefish. Then it flows mostly west to Lake Superior. There are four hydroelectric generating stations on this last section of the river (operated by Brookfield Power Inc.), and at its mouth is the Michipicoten Provincial Park that was the site of a trading post.

Magpie River (Ontario)
The Magpie River is a river in Algoma District, northeastern Ontario, Canada, The river empties into Michipicoten Bay on Lake Superior near the town of Wawa. The river drains an area of about 1,900 square kilometres (734 sq mi).
Ismaïl Omar Guelleh
Ismaïl Omar Guelleh (born 27 November 1947), often referred to by his initials IOG, is a Djiboutian politician who has served as the President of Djibouti since 1999.

Guelleh was first elected as President in 1999 as the handpicked successor to his uncle, Hassan Gouled Aptidon, who had ruled Djibouti since independence in 1977. Guelleh was re-elected in 2005, 2011, 2016 and in 2021. The elections were largely boycotted by the opposition amid complaints over widespread irregularities. Guelleh has been characterized as a dictator, and his rule has been criticized by human rights groups and foreign governments.

Hassan Gouled Aptidon
Hassan Gouled Aptidon (Somali: Xasan Guuleed Abtidoon; Arabic: حسن جوليد أبتيدون; October 15, 1916 – November 21, 2006) was a Djiboutian politician and dictator who served as the first President of Djibouti from 1977 to 1999.
Death Game 1999
"Death Game 1999" is a British comic science fiction/sport story published in the weekly anthologies Action and Battle Action from 8 May 1976 to 3 November 1979 by IPC Magazines.

The story is centred around a highly violent gladiatorial futuristic sport, played by convicted prisoners. Following the controversy which saw Action withdrawn from sale in October 1976, the story was retooled as the less violent "Spinball". After Action was folded into war comic Battle in 1977, the story was renamed a second time as "The Spinball Wars".

Action (comics)
Action was a British weekly boys' comic published by IPC Magazines from 14 February 1976 to 5 November 1977, when it merged with war comic Battle after 86 issues. The comic was created by Pat Mills and Geoff Kemp.

While initially a sales success, the comic quickly received media criticism for its violent content, causing a moral panic that ultimately saw it withdrawn from sale by IPC in October 1976, amid rumours it was to be banned. Action returned two months later in a much-sanitised form, quickly losing readers and being cancelled the following year. Despite its short lifespan, Action was highly influential on the British comics scene, and was a direct forerunner of the long-running 2000 AD.
Match of the Day
Match of the Day (abbreviated to MOTD) is a football highlights programme, typically broadcast on BBC One on Saturday nights during the Premier League season.

Match of the Day is one of the BBC's longest-running shows, having been on air since 22 August 1964. In 2015, Guinness World Records recognised it "as the longest-running football television programme in the world." Analysis is currently provided by Danny Murphy, Micah Richards and Alan Shearer, among others. Former England international striker Gary Lineker was the series' longest-serving presenter (1999—2025). From the 2004–05 season, a second programme, Match of the Day 2, has usually aired on a Sunday in the football season, featuring highlights of all the day's games, whilst showing the goals from the Saturday action.

The show's theme tune was voted the most recognised television theme in a 2010 poll conducted by the PRS.

Match of the Day 2
Match of the Day 2 was a Premier League football highlights programme. It was a companion show to Match of the Day, usually broadcast on BBC One on Sunday evenings, thus facilitating coverage of the respective week's PL matches that were played since the broadcast of the initial programme.

At the start of the 2025/26 Premier League season, the show was rebranded to be under the main Match of the Day branding. One of the main factors is that host Mark Chapman now also hosts Saturday's programme.
Mameshiba no Taigun
Mameshiba no Taigun (豆柴の大群), stylized as MAMESHiBA NO TAiGUN, is a Japanese alternative idol girl group formed through the reality survival show Monster Idol which featured on TBS Television's variety show Wednesday's Downtown in 2019. They debuted on December 19, 2019, with "Restart". They ceased activities as Mameshiba no Taigun in January 2024 after merging with Tonai Bousho to form Mameshiba no Taigun Tonai Bousho a.k.a. MonsterIdol.
In January 2025, Mameshiba no Taigun resumed activities.

Tonai Bousho
Tonai Bousho (都内某所, Somewhere in Tokyo; stylized as TONAi BOUSHO) was a Japanese alternative idol girl group formed through the reality survival show Monster Love which featured on TBS Television's variety show Wednesday's Downtown in 2022. They debuted with the single, "Cookie", on December 15, 2022. They ceased activities as Tonai Bousho in January 2024 after merging with Mameshiba no Taigun to form Mameshiba no Taigun Tonai Bousho a.k.a. MonsterIdol.
Ameena Begum (politician)
Ameena Begum, (popularly known as Dr. Ameena Shafiq) is a Bangladeshi politician and former member of parliament. She served as a member of the Jatiya Sangsad from 2001 to 2006, representing women's reserved seat-31 (national 331) for Bangladesh Jamaat-e-Islami. And The wife Of Leader of the Opposition (Bangladesh) Shafiqur Rahman

Shafiqur Rahman
Shafiqur Rahman (Bengali: শফিকুর রহমান, romanized: Śôphikur Rôhômān; born 31 October 1958) is a Bangladeshi politician and physician who has been serving as the Leader of the Opposition since February 2026 and as the ameer (party leader) of the Bangladesh Jamaat-e-Islami since 2019.

Born in Kulaura, Rahman joined politics in student life by affiliating with the JaSaD Chhatra League in 1973, followed by the Bangladesh Islami Chhatra Shibir in 1977. After graduation, he joined the Sylhet District unit of Jamaat-e-Islami party in 1984. Following ATM Azharul Islam's detention in 2011, he became the acting secretary-general of the party. In 2019, he was elected as the ameer of the party.

Rahman is known for his moderate position as a leader of an Islamist party. However, some of his remarks have become a topic of controversy.