In this task, you are given a context, a subject, a relation, and many options. Based on the context, from the options select the object entity that has the given relation with the subject. Answer with text (not indexes).
--------
Question: Context: Atlanta is the capital of and the most populous city in the U.S. state of Georgia, with an estimated 2015 population of 463,878. Atlanta is the cultural and economic center of the Atlanta metropolitan area, home to 5,710,795 people and the ninth largest metropolitan area in the United States. Atlanta is the county seat of Fulton County, and a small portion of the city extends eastward into DeKalb County., The Archdiocese of Atlanta is an archdiocese of the Catholic Church in the U.S. state of Georgia. Its ecclesiastical territory comprises Georgia's northern counties, including the capital of Atlanta. It is led by a prelate archbishop, currently Wilton D. Gregory, who is also pastor of the mother church, the Cathedral of Christ the King in Atlanta. The Cathedral is the metropolitan see of the Catholic Ecclesiastical Province of Atlanta, which covers Georgia, South Carolina, and North Carolina. As of 2014, there were 100 parishes and missions in the Archdiocese. There were 900,000 registered Catholics in the Archdiocese as of 2010., A U.S. state is a constituent political entity of the United States of America. There are 50 states, which are bound together in a union with each other. Each state holds administrative jurisdiction over a defined geographic territory, and shares its sovereignty with the United States federal government. Due to the shared sovereignty between each state and the federal government, Americans are citizens of both the federal republic and of the state in which they reside. State citizenship and residency are flexible, and no government approval is required to move between states, except for persons covered by certain types of court orders (e.g., paroled convicts and children of divorced spouses who are sharing custody)., Fayetteville is a city in Fayette County, Georgia, United States. As of the 2010 census, the city had a population of 15,945, up from 11,148 at the 2000 census. The city is the county seat of Fayette County. Fayetteville is located south of downtown Atlanta. , North Carolina is a state in the southeastern region of the United States. The state borders South Carolina and Georgia to the south, Tennessee to the west, Virginia to the north, and the Atlantic Ocean to the east. North Carolina is the 28th most extensive and the 9th most populous of the U.S. states. The state is divided into 100 counties. The capital is Raleigh. The most populous municipality is Charlotte, and it is the second largest banking center in the United States after New York City., Downtown Atlanta is the central business district of Atlanta, Georgia, United States. The largest of the city's three commercial districts, Downtown is the location of many corporate or regional headquarters; city, county, state and federal government facilities; Georgia State University; sporting venues; and most of Atlanta's tourist attractions. Downtown measures approximately four square miles, and had 26,700 residents as of 2010. Similar to other central business districts in the U.S., Downtown has recently undergone a transformation that included the construction of new condos and lofts, renovation of historic buildings, and arrival of new residents and businesses., Our Lady of Mercy Catholic High School is a private , Catholic high school in Fayetteville , Georgia . It is located in the Roman Catholic Archdiocese of Atlanta ., Subject: our lady of mercy catholic high school , Relation: inception, Options: (A) 100 (B) 11 (C) 15 (D) 2000 (E) 2010 (F) 2014 (G) 2015 (H) 50 (I) 700 (J) 710

Answer: 2000


Question: Context: The Normans (Norman: "Nourmands"; ) were the people who, in the 10th and 11th centuries, gave their name to Normandy, a region in France. They were descended from Norse ("Norman" comes from "Norseman") raiders and pirates from Denmark, Iceland and Norway who, under their leader Rollo, agreed to swear fealty to King Charles III of West Francia. Through generations of assimilation and mixing with the native Frankish and Gallo-Roman populations, their descendants would gradually adopt the Carolingian-based cultures of West Francia, ultimately resulting in their own assimilation into the Romance society. The distinct cultural and ethnic identity of the Normans emerged initially in the first half of the 10th century, and it continued to evolve over the succeeding centuries., The Church of England (C of E) is the Anglican Christian state church of England. Headed by the Archbishop of Canterbury (currently Justin Welby) and primarily governed from London with the monarch as the supreme governor, the Church of England is also the mother church of the international Anglican Communion. The church dates its formal establishment as a national church to the 6th-century Gregorian mission in Kent led by Augustine of Canterbury, with considerable features introduced and established during and following the English Reformation in the 16th century., The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a sovereign country in western Europe. Lying off the north-western coast of the European mainland, it includes the island of Great Britain (the name of which is also loosely applied to the whole country), the north-eastern part of the island of Ireland, and many smaller islands. Northern Ireland is the only part of the UK that shares a land border with another sovereign statethe Republic of Ireland. Apart from this land border, the UK is surrounded by the Atlantic Ocean, with the North Sea to its east, the English Channel to its south and the Celtic Sea to its south-south-west, giving it the 12th-longest coastline in the world. The Irish Sea lies between Great Britain and Ireland. With an area of , the UK is the 78th-largest sovereign state in the world and the 11th-largest in Europe. It is also the 21st-most populous country, with an estimated 65.1 million inhabitants. Together, this makes it the fourth most densely populated country in the European Union., Cambridge is a university city and the county town of Cambridgeshire, England, on the River Cam about north of London. At the United Kingdom Census 2011, its population was 123,867, including 24,488 students., Ridley Hall is a theological college located in Sidgwick Avenue in Cambridge in the United Kingdom, which trains men and women intending to take Holy Orders, as deacon or priest of the Church of England and the ministry of other churches. It was founded in 1881 and named in memory of Nicholas Ridley, a leading Protestant theologian of the sixteenth century. The first principal was theologian Handley Moule, later Bishop of Durham., A census of the population of the United Kingdom is taken every ten years. The 2011 census was held in all countries of the UK on 27 March 2011. It was the first UK census which could be completed online via the Internet. The Office for National Statistics (ONS) is responsible for the census in England and Wales, the General Register Office for Scotland (GROS) is responsible for the census in Scotland, and the Northern Ireland Statistics and Research Agency (NISRA) is responsible for the census in Northern Ireland., In the Christian churches, Holy Orders are ordained ministries such as bishop, priest or deacon. In the Roman Catholic (Latin: "sacri ordines"), Eastern Catholic, Eastern Orthodox ( ["hiersyn"],  ["hierateuma"],  ["Svyashchenstvo"]), Oriental Orthodox, Anglican, Assyrian, Old Catholic, Independent Catholic and some Lutheran churches, holy orders is comprised is the three ministerial orders of bishop, priest and deacon, or the sacrament or rite by which candidates are ordained to those orders. Except for Lutherans and some Anglicans, these churches regard ordination as a sacrament (the "sacramentum ordinis"). The Anglo-Catholic tradition within Anglicanism identifies more with the Roman Catholic position about the sacramental nature of ordination., Handley Carr Glyn Moule (23 December 1841  8 May 1920) was an evangelical Anglican theologian, writer, poet, and Bishop of Durham from 1901-1920. , England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west. The Irish Sea lies northwest of England and the Celtic Sea lies to the southwest. England is separated from continental Europe by the North Sea to the east and the English Channel to the south. The country covers five-eighths of the island of Great Britain (which lies in the North Atlantic) in its centre and south; and includes over 100 smaller islands such as the Isles of Scilly, and the Isle of Wight., The Bishop of Durham is the Anglican bishop responsible for the Diocese of Durham in the Province of York. The diocese is one of the oldest in England and its bishop is a member of the House of Lords. Paul Butler has been the Bishop of Durham since his election was confirmed at York Minster on 20 January 2014. The previous bishop was Justin Welby, Archbishop of Canterbury. The bishop is one of two (the other is the Bishop of Bath and Wells) who escort the sovereign at the coronation., The Bishop of Thetford is an episcopal title which takes its name after the market town of Thetford in Norfolk, England. The title was originally used by the Normans in the 11th century, and is now used by a Church of England suffragan bishop., Hugo Ferdinand de Waal ( 16 March 1935 -- 6 January 2007 ) was Principal of Ridley Hall , Cambridge from 1978 to 1991 and the suffragan Bishop of Thetford from 1992 until 2000 . He was born at Jember on East Java and educated at Tonbridge School and Pembroke College , Cambridge before embarking on an ecclesiastical career with a curacy at St Martin in the Bull Ring after which he was Chaplain at his old college then Rector of Dry Drayton . Following this he was Vicar of St John the Evangelist , Blackpool and then ( his final appointment before elevation to the Episcopate ) Principal of Ridley Hall theological college in Cambridge ( 1978 -- 91 ) . In retirement he continued to serve the Church as an honorary assistant bishop within the Diocese in Europe until his death ., The River Cam is the main river flowing through Cambridge in eastern England. After leaving Cambridge, it flows north and east into the Great Ouse to the south of Ely at Pope's Corner. The Great Ouse connects the Cam to the North Sea at King's Lynn: The total distance from Cambridge to the sea is about and is navigable for punts, small boats, and rowing craft. The Great Ouse also connects to England's canal system via the Middle Level Navigations and the River Nene. In total, the Cam runs for around from its furthest source (near Debden in Essex) to its confluence with the Great Ouse. , Subject: hugo de waal, Relation: occupation, Options: (A) archbishop (B) bishop (C) butler (D) deacon (E) general (F) king (G) leader (H) member (I) monarch (J) poet (K) priest (L) research (M) theologian (N) united kingdom

Answer: priest


Question: Context: Given a category C and a morphism f \ colon X \ to Y in C , the image of f is a monomorphism h \ colon I \ to Y satisfying the following universal property : There exists a morphism g \ colon X \ to I such that f = hg . For any object Z with a morphism k \ colon X \ to Z and a monomorphism l \ colon Z \ to Y such that f = lk , there exists a unique morphism m \ colon I \ to Z such that h = lm. Remarks : such a factorization does not necessarily exist g is unique by definition of monic ( = left invertible , abstraction of injectivity ) m is monic . h = lm already implies that m is unique . k = mg The image of f is often denoted by im f or Im ( f ) . One can show that a morphism f is epic if and only if f = im f., In the context of abstract algebra or universal algebra, a monomorphism is an injective homomorphism. A monomorphism from "X" to "Y" is often denoted with the notation formula_1., In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word "homomorphism" comes from the ancient Greek language: " (homos)" meaning "same" and " (morphe)" meaning "form" or "shape"., Category theory formalizes mathematical structure and its concepts in terms of a collection of "objects" and of "arrows" (also called morphisms). A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. The language of category theory has been used to formalize concepts of other high-level abstractions such as sets, rings, and groups., Mathematics (from Greek  "máthma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics., In various branches of mathematics, a useful construction is often viewed as the most efficient solution to a certain problem. The definition of a universal property uses the language of category theory to make this notion precise and to study it abstractly., In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras. The term "abstract algebra" was coined in the early 20th century to distinguish this area of study from the other parts of algebra., Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures.
For instance, rather than take particular groups as the object of study, in universal algebra one takes "the theory of groups" as an object of study., Subject: image , Relation: part_of, Options: (A) 20th century (B) abstract algebra (C) algebra (D) category theory (E) division (F) learning (G) mathematics (H) theory (I) universal algebra (J) word

Answer:
category theory