Homological kernels of monoidal functors

• Kevin Coulembier ^[1]
  1. [1] University of Sydney

     University of Sydney

     Australia

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 2, 2023
• Idioma: inglés
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• Resumen

  • We show that each rigid monoidal category a over a field defines a family of universal tensor categories, which together classify all faithful monoidal functors from a to tensor categories. Each of the universal tensor categories classifies monoidal functors of a given ‘homological kernel’ and can be realised as a sheaf category, not necessarily on a. This yields a theory of ‘local abelian envelopes’ which completes the notion of monoidal abelian envelopes.