Full category

This is a glossary of properties and concepts in category theory in mathematics.

Especially for higher categories, the concepts from algebraic topology are also used in the category theory. For that see also glossary of algebraic topology.

The notations and the conventions used throughout the article are:

satisfying the condition: for each morphism f: x → y in C, ${\displaystyle \phi _{y}\circ F(f)=G(f)\circ \phi _{x}}$. For example, writing ${\displaystyle GL_{n}(R)}$ for the group of invertible n-by-n matrices with coefficients in a commutative ring R, we can view ${\displaystyle GL_{n}}$ as a functor from the category CRing of commutative rings to the category Grp of groups. Similarly, ${\displaystyle R\mapsto R^{*}}$ is a functor from CRing to Grp. Then the determinant det is a natural transformation from ${\displaystyle GL_{n}}$ to -^*.

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