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Is K the same as propositional extensionality?
Judging from here: https://ncatlab.org/nlab/show/propositional+extensionality
the assertion of this equivalence is a special case of the univalence axiom
But axiom K is incompatible with univalence, because it implies Uniqueness of Identity Proofs (UIP). Wouldn't K be more like "propositional intensionality" i.e. it says two things are equal iff they are intensionally equal, because all proofs of equality are Refl?
Maybe I'm totally misunderstanding...
Looks like this fell off my watch list, somehow.
You might be right, but I'll have to think