theHigherGeometer on Nostr: Oh, this looks fun "A Categorical Approach to Forcing?" ...
Oh, this looks fun "A Categorical Approach to Forcing?"
https://www.saattrupdan.com/posts/2018-09-20-a-categorical-approach-to-forcing
"As a finishing comment we could ask if we gain anything by attempting to construct the “true” forcing category; i.e. a category consisting of cbas in which isomorphism in this category corresponds exactly to forcing equivalence. Since forcing equivalence is not the same as strong forcing equivalence there will be more isomorphisms in this category. But how can we construct such a category? One such way could be to somehow use Solovay’s characterisation of forcing equivalence to extract the weaker notion of a “forcing equivalence morphism” from this and then localise the category by these maps."
I'll have to come back to this to digest it...
https://www.saattrupdan.com/posts/2018-09-20-a-categorical-approach-to-forcing
"As a finishing comment we could ask if we gain anything by attempting to construct the “true” forcing category; i.e. a category consisting of cbas in which isomorphism in this category corresponds exactly to forcing equivalence. Since forcing equivalence is not the same as strong forcing equivalence there will be more isomorphisms in this category. But how can we construct such a category? One such way could be to somehow use Solovay’s characterisation of forcing equivalence to extract the weaker notion of a “forcing equivalence morphism” from this and then localise the category by these maps."
I'll have to come back to this to digest it...