Problem: Information: - 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 "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 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. Given the paragraphs above, decide what entity has the relation 'part of' with 'category theory'.

A: image

[Q]: Information: - The (FIFA ; "International Federation of Association Football") is the international governing body of association football, futsal, and beach soccer. FIFA is responsible for the organisation of football's major international tournaments, notably the World Cup which commenced in 1930 and the Women's World Cup which commenced in 1991. - The Union of European Football Associations (UEFA, ; ) is the administrative body for association football in Europe, although several member states are primarily or entirely located in Asia. It is one of six continental confederations of world football's governing body FIFA. UEFA consists of 55 national association members. - The UEFA Europa League, previously called the UEFA Cup, is an annual football club competition organized by UEFA since 1971 for eligible European football clubs. Clubs qualify for the competition based on their performance in their national leagues and cup competitions. - The UEFA Respect Fair Play ranking has been used by UEFA since 1995 to grant three berths for the first qualifying round of the UEFA Europa League . As of the 2015 -- 16 season it will no longer grant any berths , instead granting a monetary prize to winning associations . - Europe is a continent that comprises the westernmost part of Eurasia. Europe is bordered by the Arctic Ocean to the north, the Atlantic Ocean to the west, and the Mediterranean Sea to the south. To the east and southeast, Europe is generally considered as separated from Asia by the watershed divides of the Ural and Caucasus Mountains, the Ural River, the Caspian and Black Seas, and the waterways of the Turkish Straits. Yet the non-oceanic borders of Europea concept dating back to classical antiquityare arbitrary. The primarily physiographic term "continent" as applied to Europe also incorporates cultural and political elements whose discontinuities are not always reflected by the continent's current overland boundaries. - Association football, more commonly known as football or soccer, is a team sport played between two teams of eleven players with a spherical ball. It is played by 250 million players in over 200 countries and dependencies, making it the world's most popular sport. The game is played on a rectangular field with a goal at each end. The object of the game is to score by getting the ball into the opposing goal. Given the paragraphs above, decide what entity has the relation 'part of' with 'union of european football associations'.
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[A]:
uefa respect fair play ranking