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Hom $\omega$-categories of a computad are free

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arxiv 2402.01611 v3 pith:OS7XX2NE submitted 2024-02-02 math.CT cs.LO

Thibaut Benjamin , Ioannis Markakis This is my paper · ORCID
classification math.CTcs.LO
keywords functoromegacategoriescomputadfreepreservespropertyadjoint
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abstract

We provide a new description of the hom functor on weak $\omega$-categories, and we show that it admits a left adjoint that we call the suspension functor. We then show that the hom functor preserves the property of being free on a computad, in contrast to the hom functor for strict $\omega$-categories. Using the same technique, we define the opposite of an $\omega$-category with respect to a set of dimensions, and we show that this construction also preserves the property of being free on a computad. Finally, we show that the constructions of opposites and homs commute.

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    math.CT 2025-01 conditional novelty 7.0 of 10

    A depth-bounded naturality meta-operation in the Catt type theory constructs and machine-checks cylinder and cone composites in weak omega-categories.

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