An important diagrama

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by iarnab_kundu, Jan 2, 2019, 5:56 PM

All the algebras and rings considered are commutative. Let $A,B$ be a $C$ algebras. Suppose we have a morphism $F:A\to B$ which gives an $A$ -algebra structure on $B$ . Let $\Delta:A\otimes_C A\to A$ be a diagonal morphism, that is the map given by $a\otimes a'\mapsto aa'$ . Let $\psi:A\otimes A\to A\otimes B$ be the morphism given by $a\otimes a'\mapsto a\otimes f(a')$ . Suppose $\phi:A\otimes B\to B$ be a morphism $a\otimes b\mapsto f(a)b$ . Then the following diagram commutes, $B$ is the fiber product over....

Proof- Given a ring $R$ we consider

Cracking the Nut Open

An important diagrama

by iarnab_kundu, Jan 2, 2019, 5:56 PM

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