Semantics for the blue calculus

Posted in Category theory, Math, Quantum by Mike Stay on 2011 April 29
Blue calculus MonCat \frac{n \mbox{Cob}_2}{} 2Hilb Set (as a one object bicategory)
Types monoidal categories manifolds 2 Hilbert spaces *
Terms with one free variable monoidal functors manifolds with boundary linear functors sets
Rewrite rules monoidal natural transformation manifolds with corners linear natural transformations functions
Tensor product \boxtimes juxtaposition (disjoint union) tensor product cartesian product
(T | T'):Y where x:X is free ([[T]] \otimes_Y [[T']]):X \to Y formal sum of cobordisms with boundary from X to Y sum of linear functors disjoint union

In the MonCat column, \boxtimes is the categorified version of the tensor product of monoids.


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