Information: - In mathematics, specifically in category theory, the category of small categories, denoted by Cat, is the category whose objects are all small categories and whose morphisms are functors between categories. Cat may actually be regarded as a 2-category with natural transformations serving as 2-morphisms. - 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. - In the mathematical theory of categories , a sketch is a category D , together with a set of limit cones and a set of colimit cones . A model of the sketch in a category C is a functor M : D \ rightarrow C that takes each specified cone to a limit cone in C and each specified cocone to a colimit cocone in C. Morphisms of models are natural transformations . Sketches are a general way of specifying structures on the objects of a category , forming a category - theoretic analog to the logical concept of a theory and its models . They allow multisorted models and models in any category . Sketches were invented in 1968 by Charles Ehresmann , using a different but equivalent definition . There are still other definitions in the research literature . - Mathematics (from Greek "mathma", 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 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". - In mathematics, a functor is a type of mapping between categories arising in category theory. Functors can be thought of as homomorphisms between categories. In the category of small categories, functors can be thought of more generally as morphisms. 'sketch ' is related to which object entity through the relation of 'facet of'? Choices: - algebra - category theory - mathematics
category theory
Information: - Eysturoy (pronounced ['estroi]) meaning 'East Island' is a region and the second-largest of the Faroe Islands in the North Atlantic, both in size and population. - Morskranes is a village on the west coast of the Faroese island of Eysturoy in the Sjovar kommuna . The 2013 population was 28 . Its postal code is FO 496 . Morskranes can translate roughly as '' Moors of the Corner '' . - The Faroe Islands (Irish: "Na Scigiri") are an archipelago between the Norwegian Sea and the North Atlantic approximately halfway between Norway and Iceland, north-northwest of mainland Scotland. The area is approximately with a 2016 population of 49,188. The islands are an autonomous country within the Kingdom of Denmark. 'morskranes' is related to which object entity through the relation of 'country'? Choices: - faroe islands - iceland - norway
faroe islands
Q: Information: - A newspaper is a serial publication containing news about current events, other informative articles (listed below) about politics, sports, arts, and so on, and advertising. A newspaper is usually, but not exclusively, printed on relatively inexpensive, low-grade paper such as newsprint. The journalism organizations that publish newspapers are themselves often metonymically called newspapers. As of 2017, most newspapers are now published online as well as in print. The online versions are called online newspapers or news websites. Newspapers are typically published daily or weekly. News magazines are also weekly, but they have a magazine format. General-interest newspapers typically publish news articles and feature articles on national and international news as well as local news. The news includes political events and personalities, business and finance, crime, weather, and natural disasters; health and medicine, science, and computers and technology; sports; and entertainment, society, food and cooking, clothing and home fashion, and the arts. - Fernand Augereau ( Naintre , 23 November 1882 -- Combree , 26 July 1958 ) was a successful early twentieth century French road racing cyclist . Augereau , who was born in Naintre , participated in the 1903 Tour de France , where he finished third , and won Bordeaux -- Paris in 1904 . He was professional from 1902 to 1911 . - The 1903 Tour de France was the first cycling race set up and sponsored by the newspaper ', ancestor of the current daily, '. It ran from 1 to 19 July in six stages over , and was won by Maurice Garin. - Maurice-Francois Garin (3 March 1871 19 February 1957) was an Italian-born French road bicycle racer best known for winning the inaugural Tour de France in 1903, and for being stripped of his title in the second Tour in 1904 along with eight others, for cheating. - France, officially the French Republic, is a country with territory in western Europe and several overseas regions and territories. The European, or metropolitan, area of France extends from the Mediterranean Sea to the English Channel and the North Sea, and from the Rhine to the Atlantic Ocean. Overseas France include French Guiana on the South American continent and several island territories in the Atlantic, Pacific and Indian oceans. France spans and had a total population of almost 67 million people as of January 2017. It is a unitary semi-presidential republic with the capital in Paris, the country's largest city and main cultural and commercial centre. Other major urban centres include Marseille, Lyon, Lille, Nice, Toulouse and Bordeaux. - Combree is a commune in the Maine-et-Loire department in western France. 'fernand augereau' is related to which object entity through the relation of 'occupation'? Choices: - advertising - bicycle racer - commercial - entertainment - journalism - major - science
A: bicycle racer