SAMS Subject Classification Number: 4

In [2] a subobject of the monoidal unit object in a monoidal category for which the canonical morphism is invertible is called a subunit. Such subobjects parallel the the open subsets of a base topological space in categories like those of sheaves or Hilbert modules. This talk is meant to presents some constructions found in [2] involving subunits. Mentioned constructions endow any monoidal category with some topological intuition. The mentioned constructions are adaptation of ideas whose origins in [1].

[1] Boyarchenko M. and Drinfeld V.; Idempotents in monoidal categories,
http://www.math.uchicago.edu/~mitya/idempotents.pdf.

[2] Moliner Enrique P., Heunen C. and Tull S.; Tensor topology, Journal of Pure and Applied Mathematics 2020.