hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Splitting lemma
In mathematics, and more specifically in homological algebra, the splitting lemma states that in any abelian category, the following statements are equivalent for a short exact sequence

If any of these statements holds, the sequence is called a split exact sequence, and the sequence is said to split.

In the above short exact sequence, where the sequence splits, it allows one to refine the first isomorphism theorem, which states that:

C ≅ B/ker r ≅ B/q(A) (i.e., C isomorphic to the coimage of r or cokernel of q)

to:

B = q(A) ⊕ u(C) ≅ A ⊕ C

where the first isomorphism theorem is then just the projection onto C.

It is a categorical generalization of the rank–nullity theorem (in the form V ≅ ker T ⊕ im T) in linear algebra.

Logical equivalence
In logic and mathematics, statements  and  are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of  and  is sometimes expressed as , , , or , depending on the notation being used.
However, these symbols are also used for material equivalence, so proper interpretation would depend on the context. Logical equivalence is different from material equivalence, although the two concepts are intrinsically related.
Jenő Fuchs
Jenő Fuchs (also known as Jenő Fekete; 29 October 1882 – 14 March 1955) was a Hungarian sabre fencer. He competed at the 1908 and 1912 Olympics and won both the individual and team events at both Games. He missed the 1920 Olympics, where Hungary was not allowed to compete, and qualified for the 1924 Games but left his place in the team to younger fencers. In 1982 he was inducted into the International Jewish Sports Hall of Fame.

Fuchs studied law at the University of Budapest, defended a PhD in 1911, and became a lawyer. Apart from fencing and law, he was a top-ranked rower and bobsledder in Hungary and worked with the Budapest stock market.

Sabre (fencing)
The sabre (US English: saber, both pronounced /ˈseɪbər/) is one of the three disciplines of modern fencing alongside foil & epee. The sabre weapon is for thrusting and cutting with both the cutting edge and the back of the blade (unlike the other modern fencing weapons, the épée and foil, where a touch is scored only using the point of the blade).

The informal term sabre fencer refers to sabre fencers of both genders.
Marcel Tisserand
Marcel Jany Émile Tisserand (French: [maʁsɛl ʒani emil tisəʁɑ̃]; born 10 January 1993) is a professional footballer who plays as a defender for Sydney FC in the A-League Men. Born in France, he represents the DR Congo national team.

Meaux
Meaux (French pronunciation: [mo] ⓘ) is a commune on the river Marne in the Seine-et-Marne department in the Île-de-France region in the metropolitan area of Paris, France. It is 41.1 km (25.5 mi) east-northeast of the centre of Paris.

Meaux is, with Provins, Torcy and Fontainebleau, one of the four subprefectures (sous-préfectures) of the department of Seine-et-Marne, Melun being the prefecture. In France a subprefecture is the chef-lieu (the seat or administrative capital) of an arrondissement: Meaux is the subprefecture of the arrondissement of Meaux. It is also the chef-lieu of a smaller administrative division: the canton of Meaux. Finally, since its creation in 2003, Meaux has been the centre and the main town of an agglomeration community, the Communauté d'agglomération du Pays de Meaux.
Bollinger Mill State Historic Site
The Bollinger Mill State Historic Site is a state-owned property preserving a mill and covered bridge that pre-date the American Civil War in Burfordville, Cape Girardeau County, Missouri. The park was established in 1967 and offers mill tours and picnicking. It is managed by the Missouri Department of Natural Resources.  It includes the Burfordville Covered Bridge, which is listed on the National Register of Historic Places.

Missouri Department of Natural Resources
The Missouri Department of Natural Resources (MoDNR) is a state department of Missouri responsible for protecting, managing, and interpreting the state's natural, cultural, and energy resources. The department consists of multiple divisions including the Division of Environmental Quality, the Division of Geology and Land Survey, the Division of State Parks, the Environmental and Energy Resources Authority, and the Field Services Division. Through its State Parks Division, the department oversees and operates Missouri state parks and historic sites.
Joseph J. Rohrer Farm
Joseph J. Rohrer Farm, also known as Rohrer Place, is a historic farm and national historic district located in Harrison Township, Elkhart County, Indiana. The house was built in 1858, and is a two-story, three-bay, frame dwelling with Federal style design elements.  It has a side gable slate roof and full-width front porch.  The property also includes the contributing old house (c. 1854), bank barn (1861), chicken house, smokehouse, and corn crib.: 3

It was added to the National Register of Historic Places in 1990.

Smokehouse
A smokehouse (North American) or smokery (British) is a building where meat or fish is cured with smoke. The finished product might be stored in the building, sometimes for a year or more. Even when smoke is not used, such a building—typically a subsidiary building—is sometimes referred to as a "smokehouse".  When smoke is not used, the term meathouse or meat house is common.
DJ Wich
Tomáš Pechlák (born June 9, 1978 in Czechoslovakia), professionally known as DJ Wich, is a Czech deejay, record producer and audio engineer, who works on the Czech and Slovak hip hop scenes. He is a former member of Czech hip hop duo Indy & Wich together with Andreas "Indy" Christodoulou. He started DJing in 1998.

Rasco
Keida Brewer (born September 6, 1970), known professionally as Rasco (a bacronym for "Realistic, Ambitious, Serious, Cautious, and Organized"), is an American rapper.

Born in Cleveland, Ohio, Rasco became associated with hip hop in California. His first album was released on Stones Throw Records. He is also a member of the rap group Cali Agents with Planet Asia.
Bochorma fortress
The Bochorma fortress (Georgian: ბოჭორმის ციხე, romanized: boch'ormis tsikhe) is a medieval architectural complex in eastern Georgia, located in the Tianeti Municipality in the region of Mtskheta-Mtianeti. Historically it was part of principality of Kakheti. Situated on a high mount on the Iori River, the complex consists of a castle and a domed dodecagonal church, both dated to the 10th century, as well as another small hall church, and some other accessory structures. All structures within the complex are half-ruined or significantly damaged. They are all inscribed on the list of the Immovable Cultural Monuments of National Significance.

Iori (river)
The Iori (Georgian: იორი, Azerbaijani: Qabırrı) is a river in the South Caucasus that originates in the Greater Caucasus Mountains in eastern Georgia and flows south into Azerbaijan, where it is also known as Gabirry (Qabirry). The river eventually flows into the Mingachevir reservoir, which is drained by the Kura. It is 320 km (200 mi) long, and has a drainage basin of 4,650 km2 (1,800 sq mi). It starts in the mountains northeast of Tianeti, flows through that town, swings east and flows through the lowlands parallel to and between the Alazani (north) and the Kura (south).

In Antiquity, the river was known as the Cambyses river. This ancient name of the river was also lent to the ancient region of Cambysene.
2012 Odlum Brown Vancouver Open – Women's doubles
Karolína Plíšková and Kristýna Plíšková were the defending champions, but both were participating in the 2012 Citi Open.

Julia Glushko and Olivia Rogowska won the title defeating Jacqueline Cako and Natalie Pluskota in the final 6–4, 5–7, [10–7].

2012 Citi Open
The 2012 Citi Open (known as such for sponsorship reasons) was a tennis tournament played on outdoor hard courts. It was the 44th edition (for the men) and the 2nd edition (for the women) of the event known that year as the Citi Open (previously known on the men's tour as the Legg Mason Tennis Classic), and was part of the ATP World Tour 500 series of the 2012 ATP World Tour, and of the WTA International tournaments of the 2012 WTA Tour. It took place at the William H.G. FitzGerald Tennis Center in Washington, D.C., United States, from July 29 to August 5, 2012, running concurrently with the tennis event at the London Summer Olympics.
Antrodia ramentacea
Antrodia ramentacea is a species of polypore fungus in the family Fomitopsidaceae, first described in 1879 by Miles Joseph Berkeley and Broome and transferred into its current genus by Marinus Anton Donk in 1966.

Christopher Edmund Broome
Christopher Edmund Broome (24 July 1812 – 15 November 1886) was a British mycologist. The standard author abbreviation Broome is used to indicate this person as the author when citing a botanical name.
Rebecca Jordan-Young
Rebecca M. Jordan-Young (born 1963), is an American feminist scientist and gender studies scholar. Her research focuses on social medical science, sex, gender, sexuality, and epidemiology.  She is the Ann Whitney Olin Professor of Women's, Gender, and Sexuality Studies at Barnard College.

American Journal of Bioethics
The American Journal of Bioethics (AJOB) is a monthly peer-reviewed academic journal published by Taylor & Francis, covering all aspects of bioethics. It publishes target articles, open peer commentaries, editorials, book reviews, and case studies and commentaries in clinical care and research ethics. The journal also publishes special issues that address timely ethical challenges. The editor-in-chief is David Magnus (Stanford University), who was also one of the journals founders.

The journal was established in 1999 by founding editor-in-chief Glenn McGee and David Magnus. It has produced independently managed journals on neuroscience and empirical bioethics as spin-offs.
Bleed Magic
"Bleed Magic" is a song by American rock duo I Dont Know How but They Found Me. It was released through Fearless Records on October 26, 2018, as the third and final single for their debut EP 1981 Extended Play (2018). The song was written and produced by bassist and vocalist Dallon Weekes with David Pramik and WZRD BLD. The song discusses preying on Hollywood celebrities with an upbeat soundscape to offset it and was positively received upon release.

Drew Fulk
Drew Fulk (born May 1, 1987), also known as Wzrd Bld, is an American producer and songwriter based in Los Angeles, California. He has worked with artists such as Twenty One Pilots, Knocked Loose, Lil Peep, HEALTH, A Day To Remember, Lil Wayne, Motionless In White, and Disturbed and has over twenty #1 Billboard Rock Songs to his name. He also runs his own publishing company, In the Cut Publishing, through APG.
David Dutremble
David E. Dutremble is an American politician and firefighter from Maine. Dutremble is a Democratic State Senator from Maine's 4th District, representing part of York County, including the city of Biddeford and the neighboring towns of Kennebunkport, Arundel and Kennebunk. In 2012, he beat Independent James Booth to become State Senator, replacing fellow Democrat Nancy Sullivan, who was unable to seek re-election due to term limits. In 2012, Dutremble was named chair of the Inland Fisheries and Wildlife committee.

He resigned his seat on January 27, 2016, after already having said he would not seek reelection. He stated that he wished to focus on treatment for alcohol abuse.

Maine Senate
44°18′26″N 69°46′54″W﻿ / ﻿44.307138°N 69.781586°W﻿ / 44.307138; -69.781586

The Maine Senate is the upper house of the Maine Legislature, the state legislature of the U.S. state of Maine. The Senate currently consists of 35 members representing an equal number of districts across the state, though the Maine Constitution allows for "an odd number of Senators, not less than 31 nor more than 35". Unlike the lower House, the Senate does not set aside nonvoting seats for Native tribes.  Because it is a part-time position, members of the Maine Senate usually have outside employment as well.

The Senate meets at the Maine State House in Augusta. Members are limited to four consecutive terms with each term being two years but may run again after a two-year wait.
Rogozikha
Rogozikha (Russian: Рогозиха) is a rural locality (a selo) and the administrative center of Rogozikhinsky Selsoviet, Pavlovsky District, Altai Krai, Russia. The population was 915 as of 2013. There are 15 streets.

Altai Krai
Altai Krai (Russian: Алтайский край, IPA: [ɐlˈtajskʲɪj kraj]) is a federal subject of Russia (a krai). It borders, clockwise from the west, Kazakhstan (East Kazakhstan Region, Abai Region and Pavlodar Region), Novosibirsk and Kemerovo, and the Altai Republic. Its administrative centre is the city of Barnaul. As of the 2021 Census, the population of the krai was 2,163,693.
Kevin Dooney
Kevin Dooney (born 7 July 1993) is an Irish long-distance runner.

He competed in the men's half marathon at the 2018 IAAF World Half Marathon Championships held in Valencia, Spain. He finished in 135th place. In 2019, he competed in the senior men's race at the 2019 IAAF World Cross Country Championships held in Aarhus, Denmark. He finished in 105th place.. He won the 2018 Irish Life Health National Senior Cross Country Championship .

His father Roy was an Irish cross country and marathon runner, who finished second in the 1991 Chicago Marathon.

1991 Chicago Marathon
The 1991 Chicago Marathon was the 14th running of the annual marathon race in Chicago, United States and was held on October 27. The elite men's race was won by Brazil's Joseildo da Silva in a time of  2:14:33 hours and the women's race was won by Sweden's Midde Hamrin in 2:36:21.
1917 Edinburgh and St Andrews Universities by-election
The 1917 Edinburgh and St Andrews Universities by-election was held on 10 August 1917.  The by-election was held due to the incumbent Conservative MP, Sir Christopher Johnston, becoming a Senator of the College of Justice.  It was won by the Conservative candidate Watson Cheyne, who was unopposed due to a War-time electoral pact.

At a meeting of the electors on 10 August 1917, Sir William Watson Cheyne, Professor of Clinical Surgery at King's College, London, was elected in place of Sir Christopher Nicholson Johnston KC, who has been appointed to judicial office.

Christopher Johnston, Lord Sands
Christopher Nicholson Johnston, Lord Sands FRSE (18 October 1857 – 26 February 1934) was a Senator of the College of Justice in Scotland and Unionist Party (Scotland) MP for the Edinburgh and St Andrews Universities constituency between two by-elections in 1916 and 1917. He was an expert on Church Law and represented the Church of Scotland on many occasions.
John Hunter (Royal Navy officer)
Vice-Admiral John Hunter (29 August 1737 – 13 March 1821) was an officer of the Royal Navy, who succeeded Arthur Phillip as the second Governor of New South Wales, serving from 1795 to 1800.

Both a sailor and a scholar, he explored the Parramatta River as early as 1788, and was the first to surmise that Tasmania might be an island. As governor, he tried to combat serious abuses by the military in the face of powerful local interests led by John MacArthur. Hunter's name is commemorated in historic locations such as Hunter Valley and Hunter Street, Sydney.

Leith
Leith (/liːθ/; Scottish Gaelic: Lìte) is a suburb to the north of Edinburgh, Scotland, lying at the mouth of the Water of Leith. It is home to the Port of Leith.

The earliest surviving historical references are in the royal charter authorising the construction of Holyrood Abbey in 1128 in which it is termed Inverlet (Inverleith). After centuries of control by Edinburgh, Leith was made a separate burgh in 1833 only to be merged into Edinburgh in 1920.

Leith is located on the southern coast of the Firth of Forth and lies within the City of Edinburgh council area; since 2007 it has formed one of 17 multi-member wards of the city.
Akkihebbal Ravishankara
Akkihebbal Ramaiah (Ravi) Ravishankara ForMemRS FAAAS FRSC is a scientist specializing in Chemistry and Atmospheric Sciences, and University Distinguished Professor in the Departments of Chemistry and Atmospheric Sciences at Colorado State University, Fort Collins.

He has been a leading researcher on the chemistry of the atmosphere with special focus on stratospheric ozone depletion, climate change, and air quality. His contributions have been significant in understanding ozone layer depletion, the role chemically active species play in climate change and the lifecycle of pollutants, specifically hydrofluorocarbons (HFCs) and chlorofluorocarbons (CFCs). He was part of the assessment steering committee (2006) of and co-chaired (2010 and 2014) the World Meteorological Organization (WMO)/United Nations Environment Programme (UNEP) Science Assessment Panel on Stratospheric Ozone.

Indian Institute of Science
The Indian Institute of Science (IISc) is a public, deemed, research university for higher education and research in science, engineering, design, and management. It is located in Bengaluru, Karnataka. The institute was established in 1909 with active support from Jamsetji Tata and thus is also locally known as the Tata Institute. It was granted a deemed university status in 1958 and recognized as an Institute of Eminence in 2018.
November 7 in the Roman Martyrology
In the Roman Rite of the Catholic Church, the Roman Martyrology is a directory of liturgical commemorations for each day of the year. There are two editions of the Martyrology currently authorized for use: the 2004 edition (the most recent) and the 1960 revision of the 1956 edition (as permitted under Summorum Pontificum). The following commemorations are listed for November 7 in each respective edition:

Diocese of Utrecht (695–1580)
The historic Diocese of Utrecht was a diocese of the Latin Church (or Western) of the Catholic Church from 695 to 1580, and from 1559 archdiocese in the Low Countries before and during the Protestant Reformation.
Jo Sang-gyeong
Jo Sang-gyeong (Korean: 조상경; born March 20, 1973) is a South Korean art director and costume designer. She is known as a costume designer, for films such as Oldboy, Tazza: The High Rollers, The Host, and Modern Boy.

Tazza: The High Rollers
Tazza: The High Rollers (Korean: 타짜) is a 2006 South Korean crime film directed by Choi Dong-hoon and based on Huh Young-man and Kim Se-yeong's manhwa of the same name. Produced by Sidus FNH and distributed by CJ Entertainment, the story revolves around a group of gambling drifters involved in the Korean card game hwatu. It was a huge commercial and critical success, becoming one of South Korea's highest-grossing films and winning numerous awards. It was the second best-selling film of 2006 in South Korea, with 6,847,777 admissions nationwide.
Flag of the Central African Republic
The flag of the Republic of Central Africa (French: Drapeau de la République centrafricaine; Sango: Bendêre tî Bêafrîka) was officially adopted in 1958. It has been retained since that time with the same design, four horizontal stripes of blue, white, green and yellow, and a single vertical band of red, with a yellow five-pointed star in the upper left corner.

Ubangi-Shari
7°N 20°E﻿ / ﻿7°N 20°E﻿ / 7; 20

Ubangi-Shari (French: Oubangui-Chari) was a French colony in central Africa, a part of French Equatorial Africa. It was named after the Ubangi and Chari rivers along which it was colonised.

Established on 29 December 1903 from the Upper Ubangi (Haut-Oubangui) and Upper Shari (Haut-Chari) territories of the French Congo, it was renamed the Central African Republic (CAR) on 1 December 1958, and gained independence on 13 August 1960.
Ghaseti Bibi Mosque
Ghaseti Bibi Mosque (Bengali: ঘসেটি বিবির মসজিদ) or Ghaseti Begum’s Kuthibari is a historic mosque located in Shoula village of Kalaia Union, Bauphal Upazila, Patuakhali District, Bangladesh. It was built by Ghaseti Begum, the eldest daughter of Nawab Alivardi Khan and the aunt of Nawab Siraj ud-Daulah. It is believed that the mosque was constructed about three and a half centuries ago. At present, the mosque is under the supervision of the archaeology department.

Siraj-ud-Daulah
Mir Syed Jafar Ali Khan Mirza Muhammad Siraj-ud-Daulah (1733 – 2 July 1757), commonly known as Siraj-ud-Daulah or Siraj ud-Daula, was the last independent Nawab of the Bengal Subah. The end of his reign marked the start of the rule of the East India Company over Bengal and later almost all of the Indian subcontinent.

Siraj succeeded his maternal grandfather, Alivardi Khan as the Nawab of Bengal in April 1756 at the age of 23. Betrayed by Mir Jafar, the commander of Nawab's army, Siraj lost the Battle of Plassey on 23 June 1757. The forces of the East India Company under Robert Clive invaded and the administration of Bengal fell into the hands of the company.
Harry Herstad
Harry Herstad (12 August 1946 – 2 May 2017) is a Norwegian civil servant, sports administrator and politician for the Labour Party.

He was born and grew up in Bergen. He served as organizational director of Nordland County Municipality and Rogaland County Municipality, but is however best known for his work in his home county Hordaland, where he was managing director of Sunnhordland kraftlag before a stint as managing director of SK Brann from 1998 to 1999. He was also chief administrative officer of Stord Municipality and Hordaland County Municipality, and dean of Stord/Haugesund University College. From 2015 to his unexpected death in May 2017 he served as an elected politician, as mayor of Stord.

Rogaland County Municipality
Rogaland County Municipality (Norwegian: Rogaland fylkeskommune) is the democratically elected regional governing administration of Rogaland county, Norway. The administration is located in the city of Stavanger.

Rogfast is a major road project that is being financed by the county municipality.
Rubicon, Wisconsin
Rubicon is a town in Dodge County, Wisconsin, United States. The population was 2,005 at the 2000 census. The unincorporated communities of Rubicon and Saylesville are located in the town. The unincorporated community of Woodland is also located partially in the town.

Administrative divisions of Wisconsin
The administrative divisions of Wisconsin include counties, cities, villages and towns. In Wisconsin, all of these are units of general-purpose local government. There are also a number of special-purpose districts formed to handle regional concerns, such as school districts.

Whether a community is a city, village or town is not strictly dependent on the community's population or area, but on the form of government selected by the residents and approved by the Wisconsin State Legislature. Cities and villages can overlap county boundaries; for example, the city of Whitewater is located in Walworth and Jefferson counties.
Koshigaya
Koshigaya (越谷市, Koshigaya-shi) is a city located in Saitama Prefecture, Japan.  As of 1 January 2021, the city had an estimated population of 345,353 in 158,022 households and a population density of 5700 persons per km2. The total area of the city is 60.24 square kilometres (23.26 sq mi). It is famous for producing daruma dolls.

Daruma doll
A Daruma doll (Japanese: 達磨, romanized: daruma; IPA: [da̠ɾɯ̟ma̠]) is a hollow, round, Japanese traditional doll modeled after Bodhidharma, the founder of the Zen tradition of Buddhism. These dolls, though typically red and depicting the Indian monk, Bodhidharma, vary greatly in color and design depending on region and artist. Though considered a toy by some, Daruma has a design that is rich in symbolism and is regarded more as a talisman of good luck to the Japanese. Daruma dolls are seen as a symbol of perseverance and good luck, making them a popular gift of encouragement. The doll has also been commercialized by many Buddhist temples to use alongside the setting of goals.