Mathematics and Computation

A blog about mathematics for computers

The pullback lemma

I remember how hard it was to assimilate category theory when I was a student. A beginning student on is asking for a solution to a basic lemma about pullbacks. It really is the sort of thing one should do by oneself. Nevertheless, here it is, in gory details.

Download: pullback.pdf


The pasting law for pullbacks goes a long, long way when generalized to homotopy (type) theory.

After we had finished the discussion of principal bundle theory "in homotopy type theory" (in abstract higher topos theory) here a colleague came to me and said: I checked all your propositions and I noticed that you are essentially just using the pasting law/pullback lemma over and over and over again. And, yes, that's true. A whole lot folllows this way.

Post a comment:
Write your comment using Markdown. Use $⋯$ for inline and $$⋯$$ for display LaTeX formulas, and <pre>⋯</pre> for display code. Your E-mail address is only used to compute your Gravatar and is not stored anywhere. Comments are moderated through pull requests.