Extended field theories are local and have classifying spaces
We show that all extended functorial field theories, both topological and nontopological, are
local. We define the smooth (infinity, d)-category of bordisms with geometric data, such as …
local. We define the smooth (infinity, d)-category of bordisms with geometric data, such as …
[HTML][HTML] Model structures on finite total orders
We initiate the study of model structures on (categories induced by) lattice posets, a subject
we dub homotopical combinatorics. In the case of a finite total order [n], we enumerate all …
we dub homotopical combinatorics. In the case of a finite total order [n], we enumerate all …
A minimal model for prestacks via Koszul duality for box operads
L Hermans - arXiv preprint arXiv:2312.04185, 2023 - arxiv.org
Prestacks are algebro-geometric objects whose defining relations are far from quadratic.
Indeed, they are cubic and quartic, and moreover inhomogeneous. We show that box …
Indeed, they are cubic and quartic, and moreover inhomogeneous. We show that box …
When Bousfield localizations and homotopy idempotent functors meet again
V Carmona - arXiv preprint arXiv:2203.15849, 2022 - arxiv.org
We adopt semimodel categories to extend fundamental results related to Bousfield
localizations of model categories. More specifically, we generalize Bousfield-Friedlander …
localizations of model categories. More specifically, we generalize Bousfield-Friedlander …
On model structures relating to spectral sequences
JA Brotherston - 2022 - etheses.whiterose.ac.uk
In [CELW19] Cirici, Egas Santander, Livernet and Whitehouse define model structures on
filtered chain complexes and bicomplexes whose weak equivalences are the $ r $-weak …
filtered chain complexes and bicomplexes whose weak equivalences are the $ r $-weak …
[HTML][HTML] Motivic Toda brackets
X Dong - arXiv preprint arXiv:2402.15906, 2024 - arxiv.org
arXiv:2402.15906v1 [math.AG] 24 Feb 2024 Page 1 arXiv:2402.15906v1 [math.AG] 24 Feb
2024 Motivic Toda brackets Xiaowen Dong∗ 27th February 2024 Abstract We construct Toda …
2024 Motivic Toda brackets Xiaowen Dong∗ 27th February 2024 Abstract We construct Toda …
Spectral sequences via linear presheaves
M Livernet, S Whitehouse - arXiv preprint arXiv:2406.02777, 2024 - arxiv.org
We study homotopy theory of the category of spectral sequences with respect to the class of
weak equivalences given by maps which are quasi-isomorphisms on a fixed page. We …
weak equivalences given by maps which are quasi-isomorphisms on a fixed page. We …
Deformation classes of invertible field theories and the Freed--Hopkins conjecture
D Grady - arXiv preprint arXiv:2310.15866, 2023 - arxiv.org
We prove a conjecture of Freed and Hopkins, which relates deformation classes of reflection
positive, invertible, $ d $-dimensional extended field theories with fixed symmetry type to a …
positive, invertible, $ d $-dimensional extended field theories with fixed symmetry type to a …
[HTML][HTML] Relative plus constructions
GC Santiago, J Scherer - Expositiones Mathematicae, 2023 - Elsevier
Let h be a connective homology theory. We construct a functorial relative plus construction
as a Bousfield localization functor in the category of maps of spaces. It allows us to associate …
as a Bousfield localization functor in the category of maps of spaces. It allows us to associate …
A horn-like characterization of the fibrant objects in the minimal model structure on simplicial sets
M Feller - arXiv preprint arXiv:2201.13400, 2022 - arxiv.org
arXiv:2201.13400v3 [math.CT] 25 Apr 2023 Page 1 arXiv:2201.13400v3 [math.CT] 25 Apr 2023
A HORN-LIKE CHARACTERIZATION OF THE FIBRANT OBJECTS IN THE MINIMAL MODEL …
A HORN-LIKE CHARACTERIZATION OF THE FIBRANT OBJECTS IN THE MINIMAL MODEL …