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

1 thought on “The pullback lemma

  1. 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](–+theory,+presentations+and+applications) 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.

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