Results 41 to 50 of about 3,075 (93)
A stable splitting of factorisation homology of generalised surfaces
Journal of the London Mathematical Society, Volume 111, Issue 2, February 2025.Abstract For a manifold W$W$ and an Ed$\smash{E_{\smash{d}} }$‐algebra A$A$, the factorisation homology ∫WA$\smash{\int _W A}$ can be seen as a generalisation of the classical configuration space of labelled particles in W$W$. It carries an action by the diffeomorphism group Diff∂(W)$\mathrm{Diff}{}_\partial (W)$, and for the generalised surfaces Wg,1≔(
Florian Kranhold
wiley +1 more source
On the equivalence of Lurie's ∞$\infty$‐operads and dendroidal ∞$\infty$‐operads
Journal of Topology, Volume 17, Issue 4, December 2024.Abstract In this paper, we prove the equivalence of two symmetric monoidal ∞$\infty$‐categories of ∞$\infty$‐operads, the one defined in Lurie [Higher algebra, available at the author's homepage, http://math.ias.edu/~lurie/, September 2017 version] and the one based on dendroidal spaces.
Vladimir Hinich, Ieke Moerdijk
wiley +1 more source
Configuration spaces as commutative monoids
Bulletin of the London Mathematical Society, Volume 56, Issue 9, Page 2847-2862, September 2024.Abstract After one‐point compactification, the collection of all unordered configuration spaces of a manifold admits a commutative multiplication by superposition of configurations. We explain a simple (derived) presentation for this commutative monoid object. Using this presentation, one can quickly deduce Knudsen's formula for the rational cohomology
Oscar Randal‐Williams
wiley +1 more source
Journal of Topology, Volume 17, Issue 2, June 2024.Abstract In a 2005 paper, Casacuberta, Scevenels, and Smith construct a homotopy idempotent functor E$E$ on the category of simplicial sets with the property that whether it can be expressed as localization with respect to a map f$f$ is independent of the ZFC axioms. We show that this construction can be carried out in homotopy type theory.
J. Daniel Christensen
wiley +1 more source
Categorical notions of fibration
, 2019 Fibrations over a category $B$, introduced to category theory by Grothendieck, encode pseudo-functors $B^{op} \rightsquigarrow {\bf Cat}$, while the special case of discrete fibrations encode presheaves $B^{op} \to {\bf Set}$.
Loregian, Fosco, Riehl, Emily
core +1 more source
On the ∞$\infty$‐topos semantics of homotopy type theory
Bulletin of the London Mathematical Society, Volume 56, Issue 2, Page 461-517, February 2024.Abstract Many introductions to homotopy type theory and the univalence axiom gloss over the semantics of this new formal system in traditional set‐based foundations. This expository article, written as lecture notes to accompany a three‐part mini course delivered at the Logic and Higher Structures workshop at CIRM‐Luminy, attempt to survey the state of
Emily Riehl
wiley +1 more source
On the geometric fixed points of real topological cyclic homology
Journal of the London Mathematical Society, Volume 109, Issue 2, February 2024.Abstract We give a formula for the geometric fixed‐points spectrum of the real topological cyclic homology of a bounded below ring spectrum, as an equaliser of two maps between tensor products of modules over the norm. We then use this formula to carry out computations in the fundamental examples of spherical group rings, perfect Fp$\mathbb {F}_p ...
Emanuele Dotto +2 more
wiley +1 more source
, 2014 We define a model structure on the category GCat of small categories with an action by a finite group G by lifting the Thomason model structure on Cat.
Bohmann, Anna Marie +5 more
core
What is an equivalence in a higher category?
Bulletin of the London Mathematical Society, Volume 56, Issue 1, Page 1-58, January 2024.Abstract The purpose of this survey is to present in a uniform way the notion of equivalence between strict n$n$‐categories or (∞,n)$(\infty ,n)$‐categories, and inside a strict (n+1)$(n+1)$‐category or (∞,n+1)$(\infty ,n+1)$‐category.
Viktoriya Ozornova, Martina Rovelli
wiley +1 more source
Frames in cofibration categories [PDF]
Journal of Homotopy and Related Structures, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source