Glossary of category theory

This is a glossary of properties and concepts in category theory in mathematics. (see also Outline_of_category_theory.)
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:
C.
 \times C \to X</math> is the dual of the end of "F" and is denoted by
For example, if "R" is a ring, "M" a right "R"-module and "N" a left "R"-module, then the tensor product of "M" and "N" is
E.
 \times C \to X</math> is the limit
where formula_5 is the category (called the subdivision category of "C") whose objects are symbols formula_6 for all objects "c" and all morphisms "u" in "C" and whose morphisms are formula_7 and formula_8 if formula_9 and where formula_10 is induced by "F" so that formula_11 would go to formula_12 and formula_13 would go to formula_14. For example, for functors formula_15,
L.
 \to \mathbf{Set}</math> is
T.
 \to B</math> and formula_36 is the coend:
Y.
, \mathbf{Set}), \, X \mapsto \operatorname{Hom}_C(-, X)</math>