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Stream: learning: questions

Topic: accessible categories

Jan Pax (Mar 17 2024 at 19:37):

how here is used that $f$ is a mono to derive $f^*=f^{-1}$ ?
Snímek-obrazovky-2024-03-17-203209.png

Morgan Rogers (he/him) (Mar 17 2024 at 19:46):

The previous line shows that $f$ is a split epimorphism. A morphism which is both a mono and a split epi is an isomorphism.

Morgan Rogers (he/him) (Mar 17 2024 at 19:47):

(or more explicitly, we have $f = f \circ f^* \circ f$ implies $f^* \circ f = id$ too)