Zobrazeno 1 - 10
of 71
pro vyhledávání: '"Gurski, Nick"'
Autor:
Gurski, Nick, Johnson, Niles
This work introduces a general theory of universal pseudomorphisms and develops their connection to diagrammatic coherence. The main results give hypotheses under which pseudomorphism coherence is equivalent to the coherence theory of strict algebras
Externí odkaz:
http://arxiv.org/abs/2312.11261
We define a tensor product for permutative categories and prove a number of key properties. We show that this product makes the 2-category of permutative categories closed symmetric monoidal as a bicategory.
Comment: 84 pages
Comment: 84 pages
Externí odkaz:
http://arxiv.org/abs/2211.04464
In this paper we show that the strict and lax pullbacks of a 2-categorical opfibration along an arbitrary 2-functor are homotopy equivalent. We give two applications. First, we show that the strict fibers of an opfibration model the homotopy fibers.
Externí odkaz:
http://arxiv.org/abs/2010.11173
Publikováno v:
Journal of Pure and Applied Algebra, Volume 223, Issue 10, 2019, Pages 4348-4383
We prove that the homotopy theory of Picard 2-categories is equivalent to that of stable 2-types.
Comment: 34 pages
Comment: 34 pages
Externí odkaz:
http://arxiv.org/abs/1712.07218
Publikováno v:
Algebraic & Geometric Topology, vol. 17 (2017), pp. 2763 -- 2806
Picard 2-categories are symmetric monoidal 2-categories with invertible 0-, 1-, and 2-cells. The classifying space of a Picard 2-category $\mathcal{D}$ is an infinite loop space, the zeroth space of the $K$-theory spectrum $K\mathcal{D}$. This spectr
Externí odkaz:
http://arxiv.org/abs/1606.07032
Autor:
Bourke, John, Gurski, Nick
Publikováno v:
Appl. Categ. Structures 25 (2017), no. 4, 603-624
We discuss the folklore construction of the Gray tensor product of 2-categories as obtained by factoring the map from the funny tensor product to the cartesian product. We show that this factorisation can be obtained without using a concrete presenta
Externí odkaz:
http://arxiv.org/abs/1508.07789
Autor:
Gurski, Nick
We show that every action operad gives rise to a notion of monoidal category via the categorical version of the Borel construction, embedding action operads into the category of 2-monads on $\mathbf{Cat}$. We characterize those 2-monads in the image
Externí odkaz:
http://arxiv.org/abs/1508.04050
Publikováno v:
Homology, Homotopy and Applications, vol. 19 (2017), no. 2, pp. 89 -- 110
Constructions of spectra from symmetric monoidal categories are typically functorial with respect to strict structure-preserving maps, but often the maps of interest are merely lax monoidal. We describe conditions under which one can transport the we
Externí odkaz:
http://arxiv.org/abs/1508.00054