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