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.
Keywords: Subunits, Tensor Topology, Restriction Categories, Tensor-Restriction Categories
2020 MSC: 18M05, 18M30
Theory and Applications of Categories, Vol. 37, 2021, No. 21, pp 635-670.
Revised 2021-06-11. Original version at