We define notions of direct and inverse limits in an $ n $-category. We prove that the $ n+ 1$-
category $ nCAT'$ of fibrant $ n $-categories admits direct and inverse limits. At the end we …

We show that the quotient of a Hom‐finite triangulated category 𝒷 by the kernel of the functor
Hom𝒷 (T,−), where T is a rigid object, is preabelian. We further show that the class of regular …

We put a monoidal model category structure on the category of chain complexes of quasi-
coherent sheaves over a quasi-compact and semi-separated scheme X. The approach …

Publisher Summary This chapter discusses the trivial extensions of Abelian categories and
applications to rings. It discusses the homological dimension of a map f: FA→ B in terms of …

The use of category equivalences for the study of endomorphism rings stems from the Morita
theorem. In a sense, this theorem can be viewed as stating that if P is a finitely generated …

Let R by a right coherent ring and R-Mod denote the category of left R-modules. We show
that there is an abelian model structure on R-Mod whose cofibrant objects are precisely the …

This paper looks for Frobenius subcategories, via the separated monomorphism category
$\operatorname {smon}(Q, I,\mathscr {X}) $, and on the other hand, aims to establish an RSS …

For any exact category A with splitting idempotents, a maximal exact category T (A)
containing A as a biresolving subcategory, is constructed. Important types of exact …

We introduce the right (left) Gorenstein subcategory relative to an additive subcategory CC
of an abelian category AA, and prove that the right Gorenstein subcategory rG (G (C) G (C)) …

ENRICHED CATEGORIES AND COHOMOLOGY Page 1 Quaestiones Mathematicae 5 (19831,
265-283 Paper read at the Symposium on Categorical Algebra and Topology University of …