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Homotopy Equivalent Algebraic Structures in Multicategories and Permutative Categories
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A BSTRACT . We show that the free construction from multicategories to permuta- tive categories is a categorically-enriched non-symmetric multifunctor. Our main result then shows that the induced…
Multicategories Model All Connective Spectra
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There is a free construction from multicategories to permutative categories, left adjoint to the endomorphism multicategory construction. The main result shows that these functors induce an…
Extending homotopy theories across adjunctions
- Mathematics
- 2015
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…
Multifunctorial inverse K-theory
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A BSTRACT . We show that Mandell’s inverse K -theory functor is a categorically- enriched non-symmetric multifunctor. In particular, it preserves algebraic structures parametrized by non-symmetric…
Coherence for braided and symmetric pseudomonoids
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It is shown that these biequivalences categorify results in the theory of monoids and commutative monoids, and generalise standard coherence theorems for braided and symmetric monoidal categories.
2-categorical opfibrations, Quillen's Theorem B, and $S^{-1}S$
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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…
A T ] 5 A pr 2 01 7 STABLE POSTNIKOV DATA OF PICARD 2-CATEGORIES
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Picard 2-categories are symmetric monoidal 2-categories with invertible 0-, 1-, and 2-cells. The classifying space of a Picard 2-category D is an infinite loop space, the zeroth space of the K-theory…
Stable Postnikov data of Picard 2-categories
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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…
Supergeometry in Mathematics and Physics
- Physics, MathematicsNew Spaces in Physics
- 2015
This is a chapter for a planned collective volume entitled "New spaces in mathematics and physics" (M. Anel, G. Catren Eds.). The first part contains a short formal exposition of supergeometry as it…
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