Definable functors between triangulated categories with applications to tensor-triangular geometry and representation theory
I Bird, J Williamson - arXiv preprint arXiv:2310.02159, 2023 - arxiv.org
We systematically develop, study, and give applications of definable functors between
compactly generated triangulated categories. Such functors preserve pure triangles, pure …
compactly generated triangulated categories. Such functors preserve pure triangles, pure …
Duality pairs, phantom maps, and definability in triangulated categories
I Bird, J Williamson - arXiv preprint arXiv:2202.08113, 2022 - arxiv.org
We define duality triples and duality pairs in compactly generated triangulated categories
and investigate their properties. This enables us to give an elementary way to determine …
and investigate their properties. This enables us to give an elementary way to determine …
On Multi-Determinant Functors for Triangulated Categories
E Aldrovandi, C Lester - arXiv preprint arXiv:2305.02293, 2023 - arxiv.org
We extend Deligne's notion of determinant functor to tensor triangulated categories.
Specifically, to account for the multiexact structure of the tensor, we define a determinant …
Specifically, to account for the multiexact structure of the tensor, we define a determinant …
Positive and negative extensions in extriangulated categories
M Gorsky, H Nakaoka, Y Palu - arXiv preprint arXiv:2103.12482, 2021 - arxiv.org
We initiate the study of derived functors in the setting of extriangulated categories. By using
coends, we adapt Yoneda's theory of higher extensions to this framework. We show that …
coends, we adapt Yoneda's theory of higher extensions to this framework. We show that …
[PDF][PDF] Universal support for triangulated categories
P Balmer, PS Ocal - arXiv preprint arXiv:2308.10815, 2023 - arxiv.org
arXiv:2308.10815v1 [math.CT] 21 Aug 2023 Page 1 UNIVERSAL SUPPORT FOR
TRIANGULATED CATEGORIES PAUL BALMER AND PABLO S. OCAL Abstract. We revisit a …
TRIANGULATED CATEGORIES PAUL BALMER AND PABLO S. OCAL Abstract. We revisit a …
Formal completion of a category along a subcategory
AI Efimov - arXiv preprint arXiv:1006.4721, 2010 - arxiv.org
Following an idea of Kontsevich, we introduce and study the notion of formal completion of a
compactly generated (by a set of objects) enhanced triangulated category along a full thick …
compactly generated (by a set of objects) enhanced triangulated category along a full thick …
On exact functors for Heller triangulated categories
M Künzer - arXiv preprint arXiv:1301.0031, 2012 - arxiv.org
arXiv:1301.0031v2 [math.KT] 13 Jan 2013 On exact functors for Heller triangulated categories
Page 1 arXiv:1301.0031v2 [math.KT] 13 Jan 2013 On exact functors for Heller triangulated …
Page 1 arXiv:1301.0031v2 [math.KT] 13 Jan 2013 On exact functors for Heller triangulated …
[图书][B] Definability in monoidal additive and tensor triangulated categories
R Wagstaffe - 2021 - search.proquest.com
The aim of this thesis is to investigate definability in monoidal additive categories. Given a
monoidal finitely accessible category C, satisfying certain assumptions, we prove that there …
monoidal finitely accessible category C, satisfying certain assumptions, we prove that there …
A modular functor from state sums for finite tensor categories and their bimodules
J Fuchs, G Schaumann, C Schweigert - arXiv preprint arXiv:1911.06214, 2019 - arxiv.org
We construct a modular functor which takes its values in the monoidal bicategory of finite
categories, left exact functors and natural transformations. The modular functor is defined on …
categories, left exact functors and natural transformations. The modular functor is defined on …
Homologically finite-dimensional objects in triangulated categories
A Kuznetsov, E Shinder - arXiv preprint arXiv:2211.09418, 2022 - arxiv.org
In this paper we investigate homologically finite-dimensional objects in the derived category
of a given small dg-enhanced triangulated category. Using these we define reflexivity, hfd …
of a given small dg-enhanced triangulated category. Using these we define reflexivity, hfd …