### Classical vs Quantum Computation (Week 10)

#### Posted by John Baez

This quarter in our course on Classical vs Quantum Computation, our goal is to repair a gaping hole in the usual application of category theory to computation — especially the lambda-calculus and its quantum generalizations. We want to be able to talk about *the process of computation!* For this, we need to get serious about 2-categories…

- Week 10 (Jan. 18) - Categorifying the concept of ‘category’ to get the concept of ‘2-category’ - in detail.

Last week’s notes are here; next week’s notes are here.

Posted at January 24, 2007 9:54 PM UTC
## Re: Classical vs Quantum Computation (Week 10)

I see that here you’ve introduced the notation ‘

f°g’ with the warning that last term it was ‘gf’. I’d like to make a plea for consistency of notation, while simultaneously allowing one to use whichever order one prefers. The notation ‘g°f’, introduced by Leibniz (or at least his close followers) should be reserved for Leibniz’s order, while the notation ‘f;g’ (derived, I believe, from theoretical computer science) should be used for the opposite order. Finally, the simplified notation ‘fg’ should remain flexible, used for whichever you prefer, introduced with an explanation to avoid confusion.