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## Comments

Welcome, Ignacio! What sort of math did you do your Ph.D. on?

My lectures are meant to be very easy: no hard proofs, lots of examples, lots of explanation of key ideas. I suggest starting with Lecture 1 and moving on, using the "Syllabus" link at the top of this page.

We've been talking about preorders, which are categories with at most one morphism from one object to another. Today is my second lecture on categories.

`Welcome, Ignacio! What sort of math did you do your Ph.D. on? My lectures are meant to be very easy: no hard proofs, lots of examples, lots of explanation of key ideas. I suggest starting with Lecture 1 and moving on, using the "Syllabus" link at the top of this page. We've been talking about preorders, which are categories with at most one morphism from one object to another. Today is my second lecture on categories.`

Thanks John! My dissertation is called "Coalgebras on Measure Spaces", and it´s about (kind of) the logic of measurable spaces. But before, and after that, I did work in lattices (as posets) with additional operations, related to logic (boolean, three-valued Lukasiewicz, Heyting, Nelson algebras). I will try to contribute as best I can and catch up.

`Thanks John! My dissertation is called "Coalgebras on Measure Spaces", and it´s about (kind of) the logic of measurable spaces. But before, and after that, I did work in lattices (as posets) with additional operations, related to logic (boolean, three-valued Lukasiewicz, Heyting, Nelson algebras). I will try to contribute as best I can and catch up.`

Thank you for sharing your thesis Ignacio!

I am very interested in logic related to probability measures.

Could you point me at any axiomatizations and computational complexity results for logics over measures like you describe in Chapter 4?

`Thank you for sharing your thesis Ignacio! I am very interested in logic related to probability measures. Could you point me at any axiomatizations and computational complexity results for logics over measures like you describe in Chapter 4?`

Here´s a good paper by Goldblatt on that: https://pdfs.semanticscholar.org/e5bd/3f04504fe2ec620c3790911974ca3b6026e0.pdf

`Here´s a good paper by Goldblatt on that: https://pdfs.semanticscholar.org/e5bd/3f04504fe2ec620c3790911974ca3b6026e0.pdf`

This is a great paper, thank you Ignacio!

`This is a great paper, thank you Ignacio!`

Given your expertise I think you'll have a pretty easy time with the section on preorders, Ignacio! If you wanted to start the course late, you picked the perfect thesis topic! You probably had it all planned out.

`Given your expertise I think you'll have a pretty easy time with the section on preorders, Ignacio! If you wanted to start the course late, you picked the perfect thesis topic! You probably had it all planned out. <img src = "http://math.ucr.edu/home/baez/emoticons/tongue2.gif">`