One-sided exact categories
S Bazzoni, S Crivei - Journal of Pure and Applied Algebra, 2013 - Elsevier
One-sided exact categories appear naturally as instances of Grothendieck pretopologies. In
an additive setting they are given by considering the one-sided part of Keller's axioms …
an additive setting they are given by considering the one-sided part of Keller's axioms …
Contractibility of the stability manifold for silting-discrete algebras
D Pauksztello, M Saorín, A Zvonareva - Forum Mathematicum, 2018 - degruyter.com
We show that any bounded t-structure in the bounded derived category of a silting-discrete
algebra is algebraic, ie has a length heart with finitely many simple objects. As a corollary …
algebra is algebraic, ie has a length heart with finitely many simple objects. As a corollary …
Torsion structures, subobjects and unique filtrations in non-abelian categories
A Tattar - 2022 - kups.ub.uni-koeln.de
In this thesis we study torsion theory, subobjects and filtration properties in quasi-abelian,
exact and right triangulated categories. All such categegories fit into the larger framework of …
exact and right triangulated categories. All such categegories fit into the larger framework of …
[PDF][PDF] Module classes induced by complexes and λ-pure-injective modules
M Cortés-Izurdiaga, J Šaroch - arXiv preprint arXiv:2104.08602, 2021 - researchgate.net
We prove that, if GProj is the class of all Gorenstein projective modules over a ring R, then
GP=(GProj, GProj⊥) is a cotorsion pair. Moreover, GP is complete when all projective …
GP=(GProj, GProj⊥) is a cotorsion pair. Moreover, GP is complete when all projective …
Philosophy of contraherent cosheaves
L Positselski - arXiv preprint arXiv:2311.14179, 2023 - arxiv.org
Contraherent cosheaves are module objects over algebraic varieties defined by gluing
using the colocalization functors. Contraherent cosheaves are designed to be used for …
using the colocalization functors. Contraherent cosheaves are designed to be used for …
Approximations and locally free modules
A Slávik, J Trlifaj - Bulletin of the London Mathematical Society, 2014 - Wiley Online Library
For any set of modules S, we prove the existence of precovers (right approximations) for all
classes of modules of bounded C-resolution dimension, where C is the class of all S-filtered …
classes of modules of bounded C-resolution dimension, where C is the class of all S-filtered …
Model categories and pro-p Iwahori–Hecke modules
N Dupré, J Kohlhaase - Journal of the Institute of Mathematics of …, 2024 - cambridge.org
Let G denote a possibly discrete topological group admitting an open subgroup I which is
pro-p. If H denotes the corresponding Hecke algebra over a field k of characteristic p, then …
pro-p. If H denotes the corresponding Hecke algebra over a field k of characteristic p, then …
Flat model structures for accessible exact categories
J Kelly - arXiv preprint arXiv:2401.06679, 2024 - arxiv.org
We develop techniques for constructing model structures on chain complexes valued in
accessible exact categories, and apply this to show that for a closed symmetric monoidal …
accessible exact categories, and apply this to show that for a closed symmetric monoidal …
Locally Type FP n and n-Coherent Categories
D Bravo, J Gillespie, MA Pérez - Applied Categorical Structures, 2023 - Springer
We study finiteness conditions in Grothendieck categories by introducing the concepts of
objects of type FP n and studying their closure properties with respect to short exact …
objects of type FP n and studying their closure properties with respect to short exact …
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 …