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.

Axiom of fun choice

Posted in Fun links, Math by Mike Stay on 2011 April 14

A fun choice function is a function f defined on a collection J of jobs that must be done such that for every job j \in J, f(j) is an element of fun. The axiom of fun choice states,

For any set \displaystyle J of jobs that must be done, there exists a fun choice function defined on \displaystyle J.

This axiom asserts that one can always find the fun in any job that must be done; a theorem of Poppins deduces from this that all such jobs are games.

Monster manual

Posted in Uncategorized by Mike Stay on 2011 April 13

What magical creature lives deep in the earth’s crust and has a horrible lisp? A BATHOLITHK.

Better than anything 2

Posted in Uncategorized by Mike Stay on 2011 April 1

Better than This Week from Baez,
Better than Lou Kauffman’s knots,
Better than all of the string theory
Witten’s forgot,

Better than Feynman’s graffiti,
Better than Calabi-Yau,
Better than Pauli’s neutrino,
Better than mu and than tau,

Better than Curie, Poincaré,
And Niels and Albert at Solvay
Better than anything except being in love.