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math.CT2023
On (naturally) semifull and (semi)separable semifunctors
Lucrezia Bottegoni
The notion of semifunctor between categories, due to S. Hayashi (1985), is defined as a functor that does not necessarily preserve identities. In this paper we study how several pr…
math.CT2023
Semiseparable functors and conditions up to retracts
Alessandro Ardizzoni, Lucrezia Bottegoni
In a previous paper we introduced the concept of semiseparable functor. Here we continue our study of these functors in connection with idempotent (Cauchy) completion. To this aim,…
math.QA2023★ 2 cited
Infinitesimal braidings and pre-Cartier bialgebras
A. Ardizzoni, L. Bottegoni, A. Sciandra +1
We propose an infinitesimal counterpart to the notion of braided category. The corresponding infinitesimal braidings are natural transformations which are compatible with an underl…