## February 23, 2007

### Classical vs Quantum Computation (Week 15)

#### Posted by John Baez

In this week’s class on Classical vs. Quantum Computation, we continued to work through an example of how typed $\lambda$-calculi give cartesian closed categories:

• Week 15 (Feb. 22) - The λ-theory of commutative rings and the cartesian closed category it generates: the "free cartesian closed category on a commutative ring object". What is a cartesian closed functor from this to Set? Guess: just a commutative ring! Blog entry.

Last week’s notes are here.

Despite my promise last week, we didn’t get to the ‘typed λ-calculus for high school calculus’ this time — the students were clearly struggling with the basics of categorical logic! I should have discussed Lawvere theories before these ‘typed λ-calculi’, since cartesian categories are a simpler context than cartesian closed categories for discussing these basics. But, I’m sort of committed to focusing on closed categories of various sorts in this class.

Posted at February 23, 2007 3:25 AM UTC

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