Answer the following question: 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. After reading the paragraphs above, we are interested in knowing the entity with which 'sketch ' exhibits the relationship of 'facet of'. Find the answer from the choices below. Choices: - algebra - category theory - mathematics
Answer:
category theory