Compact closed categories and $\Gamma$-categories (with an appendix by Andr\'e Joyal)

Amit Sharma

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arXiv · 2010.09216

Compact closed categories and $\Gamma$-categories (with an appendix by Andr\'e Joyal)

Amit Sharma

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Abstract

In this paper we study compact closed categories within the context of homotopical algebra. We construct two new model category structures by localizing two (Quillen equivalent) model categories of symmetric monoidal categories with the objective of establishing the free compact closed category on one generator as a fibrant replacement of the free symmetric monoidal category on one generator, in our localized model categories. We go on to show that the fibrant objects in our model categories are compact closed categories.

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Amit Sharma. 2020-10-16. Compact closed categories and $\Gamma$-categories (with an appendix by Andr\'e Joyal). https://arxiv.org/abs/2010.09216

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