A quasi-Abelian category is an additive category with kernels and cokernels
in which every pullback of a strict epimorphism
is a strict epimorphism, and every pushout
of a strict monomorphism is a strict monomorphism.
For a morphism 
, its image is the kernel of 
, and its coimage is
the cokernel of 
. The morphism 
is strict when the induced morphism
from its coimage to its image is an isomorphism (Bridgeland
2007, pp. 328-329). Every Abelian category
is quasi-Abelian because every morphism is strict. For
the slicing 
of a Bridgeland stability condition
and an interval 
of length less than 1, the full
subcategory 
generated by the phase subcategories 
for 
under extensions is quasi-Abelian (Bridgeland 2007,
p. 330).
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