Ext Functor

More precisely, write

\mathcal C=\mathbf{Mod}(R)

for the Category of Module over

R

, a Ring . Let

A

be in

\mathcal C

and set

T(A)=\operatorname{Hom}_{\mathcal C}(A,B)

, for fixed

B

\mathcal C

R^nT

). To this end, define
:

\operatorname{Ext}_R^n(A,B)=(R^nT)(A),

P(A)
ightarrow A
ightarrow 0,

compute
:

0
ightarrow\operatorname{Hom}_{\mathcal C}(A,B)
ightarrow\operatorname{Hom}_{\mathcal C}(P(A),B),

and take the Cohomology on the righthand side.

	CATEGORIES ABOUT EXT FUNCTOR

	homological algebra

	binary operations

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