nLab
quasi-abelian category

Definition

A quasi-abelian category is an additive category admitting the kernels and the cokernels which satisfies the following conditions:

(i) the strict epimorphisms are stable by base changes,

(ii) the strict monomorphisms are stable by co-base changes

This is definition 2.1.1 in (Kashiwara).

Examples

• The category of bornological vector spaces over the complex numbers is quasi-abelian (Prosmans-Schneiders 00)

• The category of bornological abelian groups is quasi-abelian (Bambozzi 14).

Related concepts

• abelian category

• pseudo-abelian category

References

• Masaki Kashiwara, Equivariant derived category and

  representation of real semisimple Lie groups_, pdf

• Fabienne Prosmans, Jean-Pierre Schneiders, A homological study of bornological spaces, December 2000, Prepublications Mathematiques de l’Universite Paris 13, 46 (pdf)

• Federico Bambozzi, section 1 of On a generalization of affinoid varieties (arXiv:1401.5702)