5
votes
2answers
473 views

Is the Mostowski collapse natural?

The Mostowski collapse lemma (see here for a quick ref) is one of the key basic tools in the set-theory arsenal. I wonder if the collapse is natural, in the functorial sense. More precisely, is ...
6
votes
0answers
291 views

Maps between forcing posets

We all know that forcing can be seen (if you like things that way) as a category of sheaves over the poset of forcing conditions equipped with the double negation Grothendieck topology. As such it is ...
29
votes
3answers
2k views

The set-theoretic multiverse as a (bi)category

Joel Hamkin's The set-theoretic multiverse has featured in MO questions before, e.g., here and here. But I was wondering about the best category theoretic angle to take on it. In the paper Joel ...