# reperiendi

## 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.