Tensor-restriction categories

Chris Heunen, Jean-Simon Pacaud Lemay

Research output: Contribution to journalArticlepeer-review


Restriction categories were established to handle maps that are partially defined with respect to composition. Tensor topology realises that monoidal categories have an intrinsic notion of space, and deals with objects and maps that are partially defined with respect to this spatial structure. We introduce a construction that turns a firm monoidal category into a restriction category and axiomatise the monoidal restriction categories that arise this way, called tensor-restriction categories.
Original languageEnglish
Pages (from-to)635-670
Number of pages37
JournalTheory and Applications of Categories
Issue number21
Publication statusPublished - 9 Jun 2021


  • Subunits
  • Tensor Topology
  • Restriction Categories
  • Tensor-Restriction Categories


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