Tensor topology

Christiaan Heunen, Sean Tull, Pau Enrique Moliner

Research output: Contribution to journalArticlepeer-review


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 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.
Original languageEnglish
Article number106378
Number of pages36
JournalJournal of pure and applied algebra
Issue number10
Early online date1 Apr 2020
Publication statusPublished - 31 Oct 2020


  • monoidal category
  • Subunit
  • Idempotent
  • Semilattice
  • Frame

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