Locally type and -coherent categories
D Bravo, J Gillespie, MA Pérez - arXiv preprint arXiv:1908.10987, 2019 - arxiv.org
We study finiteness conditions in Grothendieck categories by introducing the concepts of
objects of type $\text {FP} _n $ and studying their closure properties with respect to short …
objects of type $\text {FP} _n $ and studying their closure properties with respect to short …
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 …
Relative Gorenstein flat modules and Foxby classes and their model structures
A model structure on a category is a formal way of introducing a homotopy theory on that
category, and if the model structure is abelian and hereditary, its homotopy category is …
category, and if the model structure is abelian and hereditary, its homotopy category is …
Gorenstein complexes and recollements from cotorsion pairs
J Gillespie - arXiv preprint arXiv:1210.0196, 2012 - arxiv.org
We describe a general correspondence between injective (resp. projective) recollements of
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …
Applications of cotorsion triples
W Ren - Communications in Algebra, 2019 - Taylor & Francis
We study homotopy categories of model categories arising from a cotorsion triple, and the
equivalences between corresponding stable categories. We characterize homological …
equivalences between corresponding stable categories. We characterize homological …
[HTML][HTML] Gorenstein complexes and recollements from cotorsion pairs
J Gillespie - Advances in Mathematics, 2016 - Elsevier
We describe a general correspondence between injective (resp. projective) recollements of
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …
Gorenstein cohomological dimension and stable categories for groups
W Ren - arXiv preprint arXiv:2206.09589, 2022 - arxiv.org
First we study the Gorenstein cohomological dimension ${\rm Gcd} _RG $ of groups $ G $
over coefficient rings $ R $, under changes of groups and rings; a characterization for …
over coefficient rings $ R $, under changes of groups and rings; a characterization for …
[HTML][HTML] Frobenius pairs in abelian categories: Correspondences with cotorsion pairs, exact model categories, and Auslander–Buchweitz contexts
Abstract We revisit Auslander–Buchweitz approximation theory and find some relations with
cotorsion pairs and model category structures. From the notion of relative generators, we …
cotorsion pairs and model category structures. From the notion of relative generators, we …
Models for homotopy categories of injectives and Gorenstein injectives
J Gillespie - Communications in Algebra, 2017 - Taylor & Francis
ABSTRACT A natural generalization of locally noetherian and locally coherent categories
leads us to define locally type FP∞ categories. They include not just all categories of …
leads us to define locally type FP∞ categories. They include not just all categories of …
Absolutely clean, level, and Gorenstein AC-injective complexes
D Bravo, J Gillespie - Communications in Algebra, 2016 - Taylor & Francis
Absolutely clean and level R-modules were introduced in and used to show how Gorenstein
homological algebra can be extended to an arbitrary ring R. This led to the notion of …
homological algebra can be extended to an arbitrary ring R. This led to the notion of …