Zobrazeno 1 - 10
of 205
pro vyhledávání: '"Tholen, Walter"'
Building on the notion of normed category as suggested by Lawvere, we introduce notions of Cauchy convergence and cocompleteness which differ from proposals in previous works. Key to our approach is to treat them consequentially as categories enriche
Externí odkaz:
http://arxiv.org/abs/2404.09032
Pursuing a new approach to the study of infinite games in combinatorics, we introduce the categories $\mathbf{Game}_{{A}}$ and $\mathbf{Game}_{{B}}$ and provide novel proofs of some classical results concerning topological games related to the dualit
Externí odkaz:
http://arxiv.org/abs/2401.03484
Quillen's notion of small object and the Gabriel-Ulmer notion of finitely presentable or generated object are fundamental in homotopy theory and categorical algebra. Do these notions always lead to rather uninteresting classes of objects in categorie
Externí odkaz:
http://arxiv.org/abs/2302.00050
Publikováno v:
Advances in Mathematics, Volume 426, 1 August 2023, 109110
We describe a pretorsion theory in the category $Cat$ of small categories: the torsion objects are the groupoids, while the torsion-free objects are the skeletal categories, i.e., those categories in which every isomorphism is an automorphism. We inf
Externí odkaz:
http://arxiv.org/abs/2207.08487
Autor:
Nejah, Amir Homayoun, Tholen, Walter
We use the ultrafilter-convergence axiomatics for topological spaces to motivate in detail a gentle categorical introduction, first to Barr's Set-based relational T-algebras, and then to Burroni's T-preorders internal to a category C, here called T-s
Externí odkaz:
http://arxiv.org/abs/2202.10278
We consider the ordinary category Span(C) of (isomorphism classes of) spans of morphisms in a category C with finite limits as needed, composed horizontally via pullback, and give a general criterion for a quotient of Span(C) to be an allegory. In pa
Externí odkaz:
http://arxiv.org/abs/2112.04599
Autor:
Perrone, Paolo, Tholen, Walter
Publikováno v:
Applied Categorical Structures, vol. 30, pages 685-753, 2022
One way of interpreting a left Kan extension is as taking a kind of "partial colimit", whereby one replaces parts of a diagram by their colimits. We make this intuition precise by means of the "partial evaluations" sitting in the so-called bar constr
Externí odkaz:
http://arxiv.org/abs/2101.04531
Autor:
Tholen, Walter, Yeganeh, Leila
Expanding on the comprehensive factorization of functors internal to a category C, under fairly mild conditions on a monad T on C we establish that this orthogonal factorization system exists even in Burroni's category Cat(T) of (internal) T-categori
Externí odkaz:
http://arxiv.org/abs/2012.08043
Autor:
Peschke, George, Tholen, Walter
The contributions of this paper are twofold. Within the framework of Grothendieck's fibrational category theory, we present a web of fundamental 2-adjunctions surrounding the formation of the category of all small diagrams in a given category and the
Externí odkaz:
http://arxiv.org/abs/2006.10890
Publikováno v:
In Advances in Mathematics 1 August 2023 426