Reflective and coreflective subcategories
Given any additive category C with split idempotents, pseudokernels and pseudocokernels,
we show that a subcategory B is coreflective if, and only if, it is precovering, closed under …
we show that a subcategory B is coreflective if, and only if, it is precovering, closed under …
[引用][C] Projectivity and subprojectivity domains in exact categories
S Crivei, R Pop - Journal of Algebra and Its Applications, 2023 - World Scientific
We generalize to exact categories some new perspectives on projectivity, which allow us to
unify a series of recent concepts from module categories or abelian categories and to obtain …
unify a series of recent concepts from module categories or abelian categories and to obtain …
Reflective subcategories
Given a full subcategory [Fscr] of a category [Ascr], the existence of left [Fscr]-approximations
(or [Fscr]-preenvelopes) completing diagrams in a unique way is equivalent to the fact that …
(or [Fscr]-preenvelopes) completing diagrams in a unique way is equivalent to the fact that …
Abelian right perpendicular subcategories in module categories
L Positselski - arXiv preprint arXiv:1705.04960, 2017 - arxiv.org
We show that an abelian category can be exactly, fully faithfully embedded into a module
category as the right perpendicular subcategory to a set of modules or module morphisms if …
category as the right perpendicular subcategory to a set of modules or module morphisms if …
[HTML][HTML] Axiomatizing subcategories of abelian categories
S Kvamme - Journal of Pure and Applied Algebra, 2022 - Elsevier
We investigate how to characterize subcategories of abelian categories in terms of intrinsic
axioms. In particular, we find axioms which characterize generating cogenerating functorially …
axioms. In particular, we find axioms which characterize generating cogenerating functorially …
Applications of exact structures in abelian categories
J Wang, Z Huang - arXiv preprint arXiv:1510.07098, 2015 - arxiv.org
In an abelian category $\mathscr {A} $ with small ${\rm Ext} $ groups, we show that there
exists a one-to-one correspondence between any two of the following: balanced pairs …
exists a one-to-one correspondence between any two of the following: balanced pairs …
[PDF][PDF] Representations of categories
M Barr - J. Pure Appl. Algebra, 1986 - math.mcgill.ca
One of the earliest theorems in category theory stated that an abelian category could be
represented faithfully by exact functors into the category Ab of abelian groups [Freyd …
represented faithfully by exact functors into the category Ab of abelian groups [Freyd …
Semibricks in extriangulated categories
L Wang, J Wei, H Zhang - Communications in Algebra, 2021 - Taylor & Francis
Let X be a semibrick in an extriangulated category C. Let T be the filtration subcategory
generated by X. We give a one-to-one correspondence between simple semibricks and …
generated by X. We give a one-to-one correspondence between simple semibricks and …
Quotients of exact categories by cluster tilting subcategories as module categories
L Demonet, Y Liu - Journal of pure and applied algebra, 2013 - Elsevier
We prove that some subquotient categories of exact categories are abelian. This
generalizes a result by Koenig–Zhu in the case of (algebraic) triangulated categories. As a …
generalizes a result by Koenig–Zhu in the case of (algebraic) triangulated categories. As a …
Composites of central extensions form a relative semi-abelian category
T Janelidze-Gray - Applied Categorical Structures, 2014 - Springer
We consider trivial and central extensions, in the sense of G. Janelidze and GM Kelly, which
are defined with respect to an adjunction between a Barr-exact category C and a Birkhoff …
are defined with respect to an adjunction between a Barr-exact category C and a Birkhoff …