Exact category

This article is about exact categories in the sense of Quillen. For exact categories in the sense of Barr, see regular category. For exact categories in the sense of Buchsbaum, see abelian category.

In mathematics, specifically in category theory, an exact category is a category equipped with short exact sequences. The concept is due to Daniel Quillen and is designed to encapsulate the properties of short exact sequences in abelian categories without requiring that morphisms actually possess kernels and cokernels, which is necessary for the usual definition of such a sequence.