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arXiv · 1605.05112

Homotopically discrete higher categorical structures

Simona Paoli
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Abstract

We introduce the notion of homotopically discrete n-fold category as an n-fold generalization of a groupoid with no non-trivial loops. We give two equivalent descriptions of this structure: in terms of a Segal-type model and in terms of iterated internal equivalence relations. We also show that homotopically discrete n-fold categories form an n-fold categorical model of 0-types.

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Simona Paoli. 2016-05-17. Homotopically discrete higher categorical structures. https://arxiv.org/abs/1605.05112

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