Bartosz Milewski on Nostr: I'm trying to decode the universal construction of the subobject classifier. We are ...

I'm trying to decode the universal construction of the subobject classifier. We are constructing \(\Omega\) together with the monic \(true \colon 1 \rightarrowtail \Omega\) such that: for any monic between two arbitrary objects \(m \colon S \rightarrowtail P\) there exist a unique \(\chi \colon P \to \Omega\) such that \(S\) is a pullback of the following diagram.

This is messing up with my brain, since normally in a pullback you are given the two southeast arrows and solve for the two northwest arrows. This is like a categorical version of a sudoku.