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arXiv · 1706.02866

A Type-Theoretical Definition of Weak ω-Categories

Eric Finster·Samuel Mimram
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Abstract

We introduce a dependent type theory whose models are weak ω-categories, generalizing Brunerie's definition of ω-groupoids. Our type theory is based on the definition of ω-categories given by Maltsiniotis, himself inspired by Grothendieck's approach to the definition of ω-groupoids. In this setup, ω-categories are defined as presheaves preserving globular colimits over a certain category, called a coherator. The coherator encodes all operations required to be present in an ω-category: both the compositions of pasting schemes as well as their coherences. Our main contribution is to provide a canonical type-theoretical characterization of pasting schemes as contexts which can be derived from inference rules. Finally, we present an implementation of a corresponding proof system.

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Eric Finster, Samuel Mimram. 2017-06-09. A Type-Theoretical Definition of Weak ω-Categories. https://arxiv.org/abs/1706.02866

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