2025/09/25 by Dutta, Arghan, Luneia, Stefano, Rovelli, Martina +1
#Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2509.21472
We provide an explicit and elementary construction of the Morita (∞,2)-category of a monoidal category which satisfies minimal conditions. We construct it as a 3-coskeletal 2-complicial set, in which the vertices encode the monoids, the edges encode the bimodules, the triangles encode the bimodule maps out of a balanced tensor product, and tetrahedra encode composition of bimodule maps. The marked edges encode invertible bimodules, and the marked triangles encode bimodule isomorphisms with a balanced tensor product.