In
category theory
Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, cate ...
, a branch of
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, a ''C''-indexed category is a
pseudofunctor
In mathematics, a pseudofunctor ''F'' is a mapping between 2-categories, or from a category to a 2-category, that is just like a functor except that F(f \circ g) = F(f) \circ F(g) and F(1) = 1 do not hold as exact equalities but only up to ''cohe ...
from ''C''
''op'' to Cat,
where Cat is a
2-category
In category theory, a strict 2-category is a category with "morphisms between morphisms", that is, where each hom-set itself carries the structure of a category. It can be formally defined as a category enriched over Cat (the category of catego ...
of categories. Any indexed category has an associated
Grothendieck construction, which gives rise to a
fibred category.
References
{{cattheory-stub
Category theory