A quasi-Abelian category is an additive category with kernels and cokernels in which pullbacks preserve strict epimorphisms and pushouts preserve strict monomorphisms. A morphism is strict when its canonical map from coimage to image is an isomorphism. Every Abelian category is quasi-Abelian because every morphism is strict. Short phase intervals of a Bridgeland stability condition form quasi-Abelian categories (Bridgeland 2007).
Quasi-Abelian Category
See also
Abelian Category, Bridgeland Stability Condition, MorphismExplore with Wolfram|Alpha
References
Bridgeland, T. "Stability Conditions on Triangulated Categories." Ann. Math. 166, 317-345, 2007. https://doi.org/10.4007/annals.2007.166.317.Cite this as:
Weisstein, Eric W. "Quasi-Abelian Category." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Quasi-AbelianCategory.html