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 prove that all semi-abelian categories with the the Smith is Huq property satisfy the
Commutator Condition (CC): higher central extensions may be characterised in terms of …

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) …

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 …

Recollements were introduced originally by Beilinson, Bernstein and Deligne to study the
derived categories of perverse sheaves, and nowadays become very powerful in …

To a big-tilting object in a complete, cocomplete abelian category with an injective
cogenerator we assign a big-cotilting object in a complete, cocomplete abelian category with …

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 …

Balanced pairs appear naturally in the realm of relative homological algebra associated with
the balance of right-derived functors of the Hom functor. Cotorsion triplets are a natural …

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The basic notions of category theory, such as limit, adjunction, and orthogonality, all involve
assertions of the existence and uniqueness of certain arrows. Weak notions arise when one …