1. X
  2. Category Theory Papers
Log inSign up
Category Theory Papers
8,781 posts
Category Theory Papers profile banner
user avatar

Category Theory Papers

@CategoryPapers
New Category Theory papers from arxiv.org: enriched categories, topoi. Thank you to arXiv for use of its open access interoperability.
arxiv.org/list/math.CT/n…
Joined October 2009
3
Following
256
Followers
RepliesRepliesMediaMedia
  • user avatar
    Category Theory Papers
    @CategoryPapers
    16h
    A pre-triangulated category which is not triangulated Xiao-Wu Chen, Jian Liu, Xue-Song Lu, Chencheng Zhang arxiv.org/abs/2608.09777 [πš–πšŠπšπš‘.π™²πšƒ πš–πšŠπšπš‘.𝙰𝙢 πš–πšŠπšπš‘.πšπšƒ]
    In this article, we construct an explicit pre-triangulated category which is not a triangulated category. Its underlying additive category is the category of finitely generated projective modules of the type-Aβ‚… preprojective algebra over Fβ‚‚, and the suspension is induced by the graph-reflection automorphism.
  • user avatar
    Category Theory Papers
    @CategoryPapers
    16h
    R-full Schreier internal categories and their directions Stefano Ambra, Andrea Montoli, Diana Rodelo arxiv.org/abs/2608.09428 [πš–πšŠπšπš‘.π™²πšƒ]
    We introduce the notion of R-full Schreier internal category, which is the monoid analogue of the notion of aspherical abelian groupoid. We associate with every R-full Schreier internal category a direction, which is a Schreier split extension with commutative and cancellative kernel. We show that this association is functorial and that such functor is a product preserving cofibration. Thanks to these properties, we equip the connected components of the fibres of such functor with canonical commutative monoid structures. Using the equivalence between Schreier internal categories and crossed semimodules of monoids, we describe these commutative monoids in terms of crossed Schreier extensions.
  • user avatar
    Category Theory Papers
    @CategoryPapers
    Aug 10
    A direction functor approach to the cohomology of small categories Stefano Ambra, Arnaud Duvieusart, Andrea Montoli arxiv.org/abs/2608.07380 [πš–πšŠπšπš‘.π™²πšƒ]
    We show how the direction functors can be used to develop a cohomology theory for Barr-exact and S-Maltsev categories, where S is a suitable class of split epimorphisms with a fixed section. Using the fact that, for any set B, the category of small categories with B as set of object is S-Maltsev with respect to the class of Schreier points, we show that the cohomology theory of small categories arising from the direction functors coincides with the one introduced by Hoff and Golasinski.
  • user avatar
    Category Theory Papers
    @CategoryPapers
    Aug 10
    On Cofiltered Limits of ∞-Categories and Adjunctions Thorger Geiß arxiv.org/abs/2608.06551 [πš–πšŠπšπš‘.π™²πšƒ πš–πšŠπšπš‘.π™°πšƒ]
    We prove that, under mild assumptions, the limit of a cofiltered diagram of ∞-categories is a reflective (resp. coreflective) localization of its oplax (resp. lax) limit. This gives rise to a number of exceptional 'stability' results for categorical properties under such limits, in particular one for adjunctions. As an application, we recover a push-pull formula describing certain filtered colimits in the ∞-category Prᴸ of presentable ∞-categories.
  • user avatar
    Category Theory Papers
    @CategoryPapers
    Aug 6
    Three results on extension dimensions of syzygy module categories Pei Luo, Zhongkui Liu arxiv.org/abs/2608.04747 [πš–πšŠπšπš‘.π™²πšƒ]
    This paper establishes three main results on the extension dimension of syzygy module categories:(1)we prove that excellent ring extensions preserve extension dimensions of syzygy module categories,including syzygy categories of modules of finite projective dimensions;(2) for cleft extensions, we investigate the behavior of extension dimensions under natural nilpotency and projective conditions;(3)for commutative Artin rings, we establish local-global characterisations for the extension dimension.

Log in or sign up for X

See what’s happening and join the conversation

Continue with phone
or
Log in with username or email
TermsΒ·PrivacyΒ·CookiesΒ·AccessibilityΒ·Ads InfoΒ·Β© 2026 X Corp.
Advertisement
Advertisement