On $n$-exact categories I: The existence and uniqueness of maximal $n$-exact structures

Abstract

This paper is the first part of a series that investigates the existence of $n$-exact structures on idempotent complete additive categories for positive integers $n$. It is shown that every idempotent complete additive category has a unique maximal $n$-exact structure. We achieve this by constructing a bijection between $n$-exact structures on a category and certain subcategories of its functor category following ideas of Enomoto.

18 pages, comments are very welcome!

Cited by in corpus (1)

• A functorial approach to $n$-abelian categories