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arXiv · 1810.01383

Tensor Topology

Pau Enrique Moliner·Chris Heunen·Sean Tull
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Abstract

A subunit in a monoidal category is a subobject of the monoidal unit for which a canonical morphism is invertible. They correspond to open subsets of a base topological space in categories such as those of sheaves or Hilbert modules. We show that under mild conditions subunits endow any monoidal category with a kind of topological intuition: there are well-behaved notions of restriction, localisation, and support, even though the subunits in general only form a semilattice. We develop universal constructions completing any monoidal category to one whose subunits universally form a lattice, preframe, or frame.

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Pau Enrique Moliner, Chris Heunen, Sean Tull. 2018-10-02. Tensor Topology. https://doi.org/10.1016/j.jpaa.2020.106378

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