The pullback of the pushforward is not necessarily the identity--consider the case where the codomain has lower dimension than the domain, for example. If your map is a local embedding, however, the result will be true.
we know that pushforward and d is commutative.
i'm confused that whether pushforward coomunicate with partial and conjugation?
what's more,i wonder whether it's true that pushforward composited with pullback is identity.
thx
The pullback of the pushforward is not necessarily the identity--consider the case where the codomain has lower dimension than the domain, for example. If your map is a local embedding, however, the result will be true.