OpenLLM-France/wikimedia huggingface dataset:
# Mac Lane coherence theorem

In category theory, a branch of mathematics, Mac Lane's coherence theorem states, in the words of Saunders Mac Lane, “every diagram commutes”. But regarding a result about certain commutative diagrams, Kelly is states as follows: "no longer be seen as constituting the essence of a coherence theorem". More precisely (cf. #Counter-example), it states every formal diagram commutes, where "formal diagram" is an analog of well-formed formulae and terms in proof theory.
The theorem can be stated as a strictification result; namely, every monoidal category is monoidally equivalent to a strict monoidal category.

## Counter-example

It is not reasonable to expect we can show literally every diagram commutes, due to the following example of Isbell.
Let ${\mathsf {Set}}_{0}\subset {\mathsf {Set}}$ be a skeleton of the category of sets and D a unique countable set in it; note $D\times D=D$ by uniqueness. Let $p:D=D\times D\to D$ be the projection onto the first factor. For any functions $f,g:D\to D$, we have $f\circ p=p\circ (f\times g)$. Now, suppose the natural isomorphisms $\alpha :X\times (Y\times Z)\simeq (X\times Y)\times Z$ are the identity; in particular, that is the case for $X=Y=Z=D$. Then for any $f,g,h:D\to D$, since $\alpha$ is the identity and is natural,
    $f\circ p=p\circ (f\times (g\times h))=p\circ \alpha \circ (f\times (g\times h))=p\circ ((f\times g)\times h)\circ \alpha =(f\times g)\circ p$.
Since $p$ is an epimorphism, this implies $f=f\times g$. Similarly, using the projection onto the second factor, we get $g=f\times g$ and so $f=g$, which is absurd.

## Proof
### Coherence condition (Monoidal category)

In monoidal category $C$, the following two conditions are called coherence conditions:
* Let a bifunctor $\otimes \colon \mathbf {C} \times \mathbf {C} \to \mathbf {C}$ called the tensor product, a natural isomorphism $\alpha _{A,B,C}$, called the associator:
    $\alpha _{A,B,C}\colon (A\otimes B)\otimes C\rightarrow A\otimes (B\otimes C)$
* Also, let $I$ an identity object and $I$ has a left identity, a natural isomorphism $\lambda _{A}$ called the left unitor:
       $\lambda _{A}:I\otimes A\rightarrow A$
    as well as, let $I$ has a right identity, a natural isomorphism $\rho _{A}$ called the right unitor:
       $\rho _{A}:A\otimes I\rightarrow A$.

### Pentagon and triangle identity

To satisfy the coherence condition, it is enough to prove just the pentagon and triangle identity, which is essentially the same as what is stated in Kelly's (1964) paper.
# Miksztal

Miksztal is a village in the administrative district of Gmina Nowe Ostrowy, within Kutno County, Łódź Voivodeship, in central Poland. It lies approximately 4 kilometres (2 mi) east of Nowe Ostrowy, 12 km (7 mi) north-west of Kutno, and 60 km (37 mi) north of the regional capital Łódź.
# Lotf-Ali Khan Daghestani

Lotf-Ali Khan Daghestani (Persian: لطفعلی خان داغستانی) was a high-ranking Safavid military commander and official of Lezgian origin. He served as commander-in-chief (sepahsalar) from 1718 to 1720, and as the governor (beglarbeg) of Fars from 22 October 1717 to December 1720.
The appointment of Lotf-Ali Khan Daghestani in 1717 as beglarbeg of Fars brought the reach of the jurisdiction of the latter province, for the first time, close to that what it had been during the tenure of Allahverdi Khan, more than a century earlier.
Lotf-Ali Khan was a nephew as well as brother-in-law of the Safavid grand vizier, Fath-Ali Khan Daghestani (1716–1720). At the time of Fath-Ali Khan's downfall, Lotf-Ali Khan was arrested and thrown into jail.
# Vale do Rio Doce (mesoregion)

Vale do Rio Doce (English: Doce River valley) is one of the twelve mesoregions of the Brazilian state of Minas Gerais. It is composed of 102 municipalities, distributed across 7 microregions.

## Demography

Largest cities in Vale do Rio Doce (mesoregion)|the Vale do Rio Doce mesoregion (IBGE 2010 census) :
| | Rank | | Microregion | Pop. | Rank | | Microregion | Pop. | |
| Governador Valadares Ipatinga | 1 | Governador Valadares | Governador Valadares | 263594 | 11 | Inhapim | Caratinga | 24294 | Coronel Fabriciano Caratinga |
| Governador Valadares Ipatinga | 2 | Ipatinga | Ipatinga | 239177 | 12 | Belo Oriente | Ipatinga | 23397 | Coronel Fabriciano Caratinga |
| Governador Valadares Ipatinga | 3 | Coronel Fabriciano | Ipatinga | 103797 | 13 | Itambacuri | Governador Valadares | 22797 | Coronel Fabriciano Caratinga |
| Governador Valadares Ipatinga | 4 | Caratinga | Caratinga | 85322 | 14 | Conselheiro Pena | Aimorés | 22232 | Coronel Fabriciano Caratinga |
| Governador Valadares Ipatinga | 5 | Timóteo | Ipatinga | 81119 | 15 | Ipanema | Aimorés | 18169 | Coronel Fabriciano Caratinga |
| Governador Valadares Ipatinga | 6 | Guanhães | Guanhães | 31266 | 16 | Peçanha | Peçanha | 17270 | Coronel Fabriciano Caratinga |
| Governador Valadares Ipatinga | 7 | Santana do Paraíso | Ipatinga | 27258 | 17 | Resplendor | Aimorés | 17099 | Coronel Fabriciano Caratinga |
| Governador Valadares Ipatinga | 8 | Mantena | Mantena | 27115 | 18 | Ipaba | Caratinga | 16692 | Coronel Fabriciano Caratinga |
| Governador Valadares Ipatinga | 9 | Mutum | Aimorés | 26672 | 19 | Sabinópolis | Guanhães | 15707 | Coronel Fabriciano Caratinga |
| Governador Valadares Ipatinga | 10 | Aimorés | Aimorés | 24969 | 20 | São João Evangelista | Guanhães | 15538 | Coronel Fabriciano Caratinga |
# Latin American Federation of Journalists

The Latin American Federation of Journalists (Spanish: Federación Latinoamericana de Periodistas, FELAP), founded on June 7, 1976, is an association that represents journalism organizations—federations, unions, circles, and schools—in Latin America and the Caribbean, representing more than 80,000 journalists in the region as of 2012.

## Background

Its founding president was Eleazar Díaz Rangel [es], of Venezuela, and its founding general secretary was Genaro Carnero Checa [es], of Peru.
FELAP also serves as an umbrella for more than 50 associated institutions that are involved in the study and practice of communication and journalism, such as research centers, journalism schools, specialized libraries, news agencies, and publications. At the request of FELAP and the International Federation of Journalists, in 1991 the Commission for the Investigation of Attacks Against Journalists [es] was founded as a regional body working to ensure the safety of FELAP members.
In addition to its official website, FELAP has published articles on the website of the Voltaire Network. It is associated with UNESCO as a nongovernmental organization. It has worked in collaboration with many organizations, including the Argentine Media Observatory, the Union of Journalists of Buenos Aires, the Puerto Rico Journalists Association, the Chilean College of Journalists [es], the Brazilian National Federation of Journalists [pt], the Federation of Associations of Mexican Journalists, and Democracy Now. Representatives from FELAP have served on the jury for the Miguel de Cervantes Prize.
# Johanna Brenner

Johanna Brenner is an American feminist and sociologist whose writing and thought is in the socialist-feminist vein.
A graduate of Reed College (B.A., 1964) and the University of California, Los Angeles (M.A., 1970; Ph.D., 1979), she spent four years as a telephone installation technician worker in the 1970s. In 1981 she began teaching in the sociology department at Portland State University in Portland, Oregon, where she served from 1982 to 2005 as coordinator of its women's studies program. She is now emeritus professor.
Brenner has contributed to New Left Review, Monthly Review, and other periodicals. In 1993 she worked with Catherine Sameh and Kathryn Tetrick to open In Other Words Women's Books and Resources.
Mike Davis has said, "Johanna Brenner writes with a clarity of purpose that arises out of a lifetime of participation in the struggles of working-class women."
# 1981 NCAA Division I women's volleyball tournament

The 1981 NCAA Division I women's volleyball tournament was the first year that the NCAA sponsored women's volleyball, following 12 years in which the AIAW conducted the women's national intercollegiate championships. The tournament consisted of just 20 teams.
The Final Four was held on the campus of UCLA, where the heavily favored Bruins lost in the national title match against Southern California in five games: 9-15, 15-7, 10-15, 15-13, 15-7. Southern California finished the year 27-10.
In the consolation match, San Diego State swept Pacific, 3-0, to claim third place.

## Regionals
### Northwest regional

| Quarterfinals | Quarterfinals | Semifinals | Semifinals | Finals | Finals |
| | | Hawaiʻi | 3 | | |
| | | Texas A&M | 0 | | |
| Pepperdine | 1 | Texas A&M | 0 | | |
| Texas A&M | 3 | | | | |
| Texas A&M | 3 | | | Hawaiʻi | 1 |
| | | | | USC | 3 |
| | | Arizona | 0 | | |
| | | USC | 3 | | |

### Mideast regional

| Quarterfinals | Quarterfinals | Semifinals | Semifinals | Finals | Finals |
| | | Pacific | 3 | | |
| | | Penn State | 2 | | |
| Penn State | 3 | Penn State | 2 | | |
| Cincinnati | 0 | | | | |
| Cincinnati | 0 | | | Pacific | 3 |
| | | | | Cal Poly | 1 |
| | | Cal Poly | 3 | | |
| | | Northwestern | 0 | | |

### South regional

| Quarterfinals | Quarterfinals | Semifinals | Semifinals | Finals | Finals |
| | | UCLA | 3 | | |
| | | Purdue | 2 | | |
| Purdue | 3 | Purdue | 2 | | |
| Tennessee | 0 | | | | |
| Tennessee | 0 | | | UCLA | 3 |
| | | | | Stanford | 2 |
| | | Stanford | 3 | | |
| | | Arizona State | 0 | | |

### West regional

| Quarterfinals | Quarterfinals | Semifinals | Semifinals | Finals | Finals |
| | | San Diego State | 3 | | |
| | | New Mexico | 1 | | |
| New Mexico | 3 | New Mexico | 1 | | |
| Miami (OH) | 0 | | | | |
| Miami (OH) | 0 | | | San Diego State | 3 |
| | | | | UC Santa Barbara | 0 |
| | | BYU | 2 | | |
| | | UC Santa Barbara | 3 | | |

## Final Four – Pauley Pavilion, Los Angeles

| Semifinals | Semifinals | Finals | Finals |
| UCLA | 3 | | |
| San Diego State | 1 | | |
| San Diego State | 1 | UCLA | 2 |
| | | USC | 3 |
| USC | 3 | USC | 3 |
| Pacific | 2 | Third place | Third place |
| | | San Diego State | 3 |
| | | Pacific | 0 |

## NCAA Tournament record

There is one NCAA tournament record that was set during the 1981 tournament that still stands today.
* Solo blocks, tournament (individual record) - Jayne Gibson, Pacific - 15 (2 vs. Penn State, 4 vs. Cal Poly, 6 vs. Southern California, 3 vs. San Diego State)
# Cedar Island National Wildlife Refuge

Cedar Island National Wildlife Refuge, located in Carteret County, North Carolina, is on the end of a peninsula marking the southern end of Pamlico Sound. The refuge lies five miles (8 km) east of the Atlantic Ocean and about 40 miles (64 km) northeast of Beaufort, North Carolina. Established in 1964, the refuge consists of approximately 11,000 acres (45 km$^2$) of irregularly flooded, brackish marsh and 3,480 acres (14.1 km$^2$) of pocosin and woodland habitat. The dominant marsh plants include black needlerush, saltmarsh cordgrass, saltmeadow hay, and saltgrass. The woodland areas are dominated by loblolly, longleaf and pond pine. Live oak is also abundant on some upland sites. The marsh and surrounding waters provide wintering habitat for thousands of ducks and nesting habitat for colonial waterbirds.
Mammalian species that inhabit this refuge are gray squirrel, marsh rabbit, white-tailed deer, red fox, raccoon, bobcat, gray fox, nutria, beaver, muskrat, river otter, mink and opossum.
# Milejów, Wieluń County

Milejów is a village in the administrative district of Gmina Ostrówek, within Wieluń County, Łódź Voivodeship, in central Poland. It lies approximately 5 kilometres (3 mi) north-west of Ostrówek, 16 km (10 mi) north of Wieluń, and 77 km (48 mi) south-west of the regional capital Łódź.
# Roman Catholic Diocese of São Mateus

18°42′56″S 39°51′43″W﻿ / ﻿18.7156°S 39.8619°W﻿ / -18.7156; -39.8619
The Roman Catholic Diocese of São Mateus (Latin: Dioecesis Sancti Matthaei) is a diocese located in the city of São Mateus in the ecclesiastical province of Vitória in Brazil.

## History

* 16 February 1958: Established as Diocese of São Mateus from the Diocese of Espírito Santo

## Leadership

* Bishops of São Mateus (Roman rite)
** Bishop José Dalvit, M.C.C.I. (1959.05.09 – 1970.05.14)
** Bishop Aldo Gerna, M.C.C.I. (1971.05.18 – 2007.10.03)
** Bishop Zanoni Demettino Castro (2007.10.03 – 2014.12.03)
** Bishop Paulo Bosi Dal'Bó (2015.10.21 – present)
# Excelsior, McDowell County, West Virginia

Excelsior is a community incorporated within the city of War in McDowell County, West Virginia. Excelsior is located along Dry Fork to the north of the city along West Virginia Route 16.
* This article about a location in McDowell County, West Virginia is a stub. You can help Wikipedia by expanding it.
* v
* t
* e
# 613

Year 613 (DCXIII) was a common year starting on Monday of the Julian calendar. The denomination 613 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.

## Events
### By place
#### Byzantine Empire

* Emperor Heraclius marries his niece Martina; she becomes empress (Augusta) of the Byzantine Empire. This second marriage is considered to fall within the prohibited degree of kinship, and is approved by the Catholic Church in Constantinople.
* January 22 – Constantine is crowned co-emperor (Caesar) by his father Heraclius and shortly after betrothed to his cousin, Gregoria, daughter of Nicetas. Only 8 months old, Constantine has no real power and his dynastic title is purely ceremonial.
* Byzantine–Persian War: Heraclius appoints himself commander-in-chief, along with his brother Theodore (curopalates), to solidify command of the army.
* Battle of Antioch: Heraclius mobilises a Byzantine expeditionary force to Antioch (Syria), but is completely defeated outside the city by the Persians. Shahin Vahmanzadegan makes further inroads into Central and Western Anatolia. In Syria, Shahrbaraz captures the cities of Damascus, Apamea and Emesa.

#### Europe

* King Theuderic II dies of dysentery in the Austrasian capital of Metz, while preparing a campaign against his longtime enemy, Chlothar II. His grandmother Brunhilda attempts to establish a third regency for her illegitimate great-grandson Sigebert II.
* Chlothar II reunites the Frankish Kingdom by ordering the murder of Sigebert II. He accuses Brunhilda, age 70, of killing ten kings of the Franks (according to the Liber Historiae Francorum). She is dragged to death behind a wild horse at Abbeville.

#### Britain

* Battle of Chester: King Æthelfrith of Northumbria invades Gwynedd (northwest Wales), in order to route out his old enemy, Edwin of Deira. A united Brythonic force (Gwynedd, Powys, Pengwern and Dumnonian warriors) is defeated near Chester.

#### Asia

* Goguryeo–Sui War: Emperor Yángdi crosses the Liao River again, and puts Manchuria under siege. During the campaign Yang Xuangan, an official of the Sui dynasty, starts a rebellion near Luoyang. Fearing attacks from two fronts, Yángdi is forced to retreat his army.
* Isanapura becomes the capital of the Cambodian kingdom of Chenla (approximate date).

### By topic
#### Religion

* Islam: Muhammad begins preaching in public. He spreads the message of Islam and encourages a personal devotion to God. Quraysh leaders of Mecca oppose any change in the traditional tribal and religious customs.

## Births

* Woncheuk, Korean Buddhist monk (d. 696)
* Aisha, wife of Muhammad (d. 678)

## Deaths

* April 22 – Saint Theodore of Sykeon, Byzantine ascetic
* Bledric ap Custennin, king of Dumnonia (England)
* Brunhilda, queen of Austrasia
* Priscus, Byzantine general
* Sigebert II, king of Austrasia
* Theuderic II, king of Austrasia
* Uncelen, Duke of Alemannia (Germany)
* Yang Xuangan, official of the Sui dynasty
# 19 BC

Year 19 BC was either a common year starting on Thursday, Friday or Saturday or a leap year starting on Thursday or Friday of the Julian calendar (the sources differ, see leap year error for further information) and a common year starting on Wednesday of the Proleptic Julian calendar. At the time, it was known as the Year of the Consulship of Saturninus and Vespillo (or, less frequently, year 735 Ab urbe condita). The denomination 19 BC for this year has been used since the early medieval period, when the Anno Domini calendar era became the main method in Europe for naming years.

## Events
### By place
#### Roman Empire

* The Aeneid by the Roman poet Virgil is published after his death. The Aeneid is an epic poem in 12 books that tells the story of the foundation of Rome from the ashes of Troy.
* In Rome, Lucius Cornelius Balbus receives the honor of a triumph on the Forum Romanum, for his victories over the Garamantes in Africa.
* Marcus Vipsanius Agrippa completes the Aqua Virgo; the aqueduct is 21 km (13 mi) in length and supplies the city of Rome with about 100,000,000 liters of water every day.
* The Cantabrians, living on the northernmost coast of Spain, are brought under Roman control. The region is completely subdued until 16 BC.

#### Asia

* King Yuri becomes ruler of the Korean kingdom of Goguryeo.

## Births

* Vipsania Julia Agrippina, daughter of Marcus Vipsanius Agrippa and Julia the Elder

## Deaths

* September 21 – Virgil, Roman poet (b. 70 BC)
* Albius Tibullus, Roman poet (b. 54 BC)
* Dongmyeong, Korean king of Goguryeo
# Charles M. Russell National Wildlife Refuge Complex

Charles M. Russell National Wildlife Refuge Complex consists of six National Wildlife Refuges, all of them managed by the U.S. Fish and Wildlife Service. The refuges are located in the central sections of the U.S. state of Montana. The complex includes the following areas:
* Charles M. Russell National Wildlife Refuge (headquarters for the complex)
* Grass Lake National Wildlife Refuge (formerly Halfbreed Lake NWR)
* Hailstone National Wildlife Refuge
* Lake Mason National Wildlife Refuge
* War Horse National Wildlife Refuge
* UL Bend National Wildlife Refuge
# Smoking companion set

A smoking companion set or smoke set, is an object both decorative and useful. It has compartments for cigars, cigarettes, matches, ashtrays and burned matches.
They were popular in Europe circa 1900.
# 2006 NCAA Division I Outdoor Track and Field Championships

The 2006 NCAA Division I Outdoor Track and Field Championships were contested at the 85th annual NCAA-sanctioned track meet to determine the individual and team champions of men's and women's Division I collegiate outdoor track and field in the United States.
This year's meet, the 25th with both men's and women's championships, was held June 7–10, 2006 at Hornet Stadium at Sacramento State University in Sacramento, California.
Florida State won the men's title, the Seminoles' first.
Auburn won the women's title, the Tigers' first.

## Team results

* Note: Top 10 only
* (DC) = Defending champions
* Full results
# Angels Gate

Angels Gate is a 6,761-foot (2,061 m)-elevation summit located in the Grand Canyon, in Coconino County of Arizona, United States. It is situated seven miles (11 km) due north of the Grandview Point overlook on the canyon's South Rim, three miles (4.8 km) west of Vishnu Temple, and three point five miles (5.6 km) southeast of Zoroaster Temple. Topographic relief is significant as it rises over 4,200 feet (1,300 m) above the Colorado River in three miles. Angels Gate is the place in Paiute mythology where the gods would return to Earth by descending from the shadow world above.
George Wharton James applied the "Angel Gate" name to this geographical feature in his book, In & Around the Grand Canyon, in 1900. This feature's name was officially adopted in 1906 by the U.S. Board on Geographic Names. Angels Gate has four peaks composed of Coconino Sandstone. The main highest summit and three spires are known as "Snoopy and his Doghouse" for a resemblance to Snoopy, and the first ascent was made April 1972 by Chuck Graf and Dave Ganci. According to the Köppen climate classification system, Angels Gate is located in a cold semi-arid climate zone.

## Geology

The summit of Angels Gate is composed of remnant, cliff-forming, Permian Coconino Sandstone. The sandstone, which is the third-youngest of the strata in the Grand Canyon, was deposited 265 million years ago as sand dunes. Below the Coconino Sandstone is slope-forming, Permian Hermit Formation, which in turn overlays the Pennsylvanian-Permian Supai Group. Further down are strata of Mississippian Redwall Limestone, Cambrian Tonto Group, and finally Proterozoic Unkar Group at creek level and Granite Gorge. Precipitation runoff from Angels Gate drains south to the Colorado River.

## Gallery

* Northwest aspect
* Angels Gate, with Deva Temple behind
* South aspect
* From the southeast
* Wotans Throne behind Angels Gate
* Sunset from Desert View, Angels Gate (lower left of center)
* Wotans Throne (left) and Angels Gate from west on Tonto Trail
* Angels Gate from Desert View
* Angels Gate from south, circa 1901
* Angels Gate (centered)

## Hawkins Butte

Hawkins Butte is a 5,340-foot (1,630 m)-elevation butte attached at the southwest end of Angels Gate. It was officially named in 1932 after William "Billy" Robert Hawkins, the hunter and cook for John Wesley Powell's 1869 expedition down the Colorado River through the Grand Canyon. It is primarily composed of exposed cliffs of Redwall Limestone overlaying Tonto Group.
# Dorothy Zellner

Dorothy "Dottie" Miller Zellner (born 1938) is an American human rights activist, feminist, editor, lecturer, and writer. A veteran of the 1960s civil rights movement, she served as a recruiter for the Freedom Summer project and was co-editor of Student Voice, the student newsletter of the Student Nonviolent Coordinating Committee. She is active in the Palestinian solidarity movement.

## Early life

Zellner was born in Manhattan and raised by left-wing secular non-Zionist Jewish immigrant parents who could speak Yiddish. Her parents raised her with an awareness of Black history, racial justice, socialism, the Soviet Union, and Jewish resistance to Nazism. She credits the Jewish social justice tradition of her parents for inspiring her to become involved in the civil rights movement. Zellner graduated from Queens College. Zellner is "100% atheist".

## Political activism

In 1966, Zellner helped design the logo for the Black Panther Party. She was asked by Stokely Carmichael to go to Zoo Atlanta and photograph a panther for inspiration. Her husband Bob Zellner and another SNCC member took photographs and Zellner created a sketch. Carmichael requested that Zellner make another attempt based on a rough drawing by SNCC member Ruth Howard that Howard had based on the mascot of Clark Atlanta University. In 1967, Zellner's second drawing become the official Black Panther Party logo.
In 1969, while serving as a staff member of the Southern Conference Educational Fund (SCEF), Zellner wrote a memo critiquing feminist consciousness-raising groups as "therapy" and for being insufficiently "political." In response, fellow SCEF member Carol Hanisch addressed an essay to the women's caucus of the SCEF in February 1969. Originally titled "Some Thoughts in Response to Dottie’s Thoughts on a Women’s Liberation Movement", the article was republished in 1970 in the book Notes from the Second Year: Women's Liberation under the title "The Personal is Political." The essay has since become widely circulated in feminist circles.
Zellner worked as a nurse for several years, before she joined the Center for Constitutional Rights in 1984. She became director of publications and development for Queens College School of Law in 1998.
After hearing a talk by Israeli peace activist Uri Avnery in 2002, Zellner became involved in the Israeli-Palestinian peace movement. Since 2002, she has traveled to Israel and Palestine on dozens of occasions, volunteered with Physicians for Human Rights, and is an active supporter of the Boycott, Divestment and Sanctions movement (BDS).