Work

Hom ω$\omega$‐categories of a computad are free

Year: 2025

Type: article

Abstract: We provide a new description of the hom functor on weak ‐categories, and 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 ‐categories. Using the same technique, we define the opposite of an ‐category with respect to a set of dimensions, and 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.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70367

Authors: Thibaut Benjamin, Ioannis Markakis

Institutions: Centre National de la Recherche Scientifique, Université Paris-Saclay, Laboratoire Méthodes Formelles, University of Cambridge

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funder: Alexander S. Onassis Public Benefit Foundation