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Pré-Publication, Document De Travail Année : 2019

An implementation of polygraphs

Résumé

Polygraphs are a higher dimensional structure which serves as a system of generators for higher categories. They are in particular used in higher dimensional rewriting, where they are used to present strict ∞-categories. However, any notion of higher dimensional structure (e.g. weak or strict ∞-categories or groupoids) comes with its own notion of polygraph. In this paper, we describe an experimental implementation of polygraphs using the proof assistant Coq and prove some of their properties, following the types-as-∞-groupoids interpretation of homotopy type theory. We describe in particular a functor sending any polygraph to the free type it generates and parts of the adjunction between polygraphs and types.
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Dates et versions

hal-02385110 , version 1 (28-11-2019)

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  • HAL Id : hal-02385110 , version 1

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Maxime Lucas. An implementation of polygraphs. 2019. ⟨hal-02385110⟩
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