Given a regular epimorphism f: X↠ Y in an exact homological category C, and a pair (U, V) of
kernel subobjects of X, we show that the quotient (f (U)∩ f (V))/f (U∩ V) is always abelian …

We introduce relative homological and weakly homological categories,
where``relative''refers to a distinguished class of normal epimorphisms. It is a generalization …

We construct derived functors in additive categories in which each morphism has a kernel,
co-kernel, image, and coimage, but the image and coimage are not necessarily isomorphic …

We fill a gap in the literature regarding 'transport of structure'for (n+ 2)-angulated, n-exact, n-
abelian and n-exangulated categories appearing in (classical and higher) homological …

arXiv:0710.5065v3 [math.AT] 28 Oct 2008 Page 1 arXiv:0710.5065v3 [math.AT] 28 Oct 2008
ON DERIVED CATEGORIES AND DERIVED FUNCTORS SAMSON SANEBLIDZE Abstract …

According to Auslander's formula, one way of studying an abelian category C is to study mod-
C, which has nicer homological properties than C, and then translate the results back to C …

One of the most imporant results in abelian categories is the full exact embedding theorem
of Freyd, Gabriel, Lubkin, and Mitchell. In several cases, however (eg, spectral sequences in …

Let G be an object of a finitely cocomplete homological category C. We study actions of G on
objects A of C (defined by Bourn and Janelidze as being algebras over a certain monad TG) …

In finitely cocomplete homological categories, co-smash products give rise to (possibly
higher-order) commutators of subobjects. We use binary and ternary co-smash products and …

We study a property (P) of pushouts of regular epimorphisms along monomorphisms in a
regular context. We prove that (P) characterizes abelian categories among homological …