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arXiv · 2402.01611

Hom $ω$-categories of a computad are free

Thibaut Benjamin·Ioannis Markakis
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Abstract

We provide a new description of the hom functor on weak $ω$-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 $ω$-categories. Using the same technique, we define the opposite of an $ω$-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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Thibaut Benjamin, Ioannis Markakis. 2024-11-13. Hom $ω$-categories of a computad are free. https://arxiv.org/abs/2402.01611

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