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 …

Higher homological algebra was introduced by Iyama. It is also known as-homological
algebra where is a fixed integer, and it deals with-cluster tilting subcategories of abelian …

We introduce n-abelian and n-exact categories, these are analogs of abelian and exact
categories from the point of view of higher homological algebra. We show that n-cluster …

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 …

This article develops several main results for a general theory of homological algebra in
categories such as the category of sheaves of idempotent modules over a topos. In the …

Classical homological algebra takes place in additive categories. In homotopy theory such
additive categories arise as homotopy categories of “additive groupoid enriched categories” …

We prove that the localizations of the categories of dg categories, of cohomologically unital
and strictly unital $ A_\infty $ categories with respect to the corresponding classes of quasi …

For a locally presentable abelian category B with a projective generator, we construct the
projective derived and contraderived model structures on the category of complexes …

In this paper, we study the homological theory in n-abelian categories. First, we prove some
useful properties of n-abelian categories, such as (n+ 2) * (n+ 2)(n+ 2)×(n+ 2)-lemma, 5 …

We survey the basics of homological algebra in exact categories in the sense of Quillen. All
diagram lemmas are proved directly from the axioms, notably the five lemma, the 3× 3 …