Ext Functor

In mathematics, the Ext functors of homological algebra are derived functors of \mathrm{Hom} functors. They were first used in algebraic topology, but are common in many areas of mathematics. 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)=\mathrm{Hom}_{\mathcal C}(A,B), for fixed B in \mathcal C. (This is a left exact functor (contravariant) so we want its right derived functors R^nT). To this end, define
\mathrm{Ext}_R^n(A,B)=(R^nT)(A),
i.e., take a projective resolution
P(A)\rightarrow A\rightarrow 0,
compute
0\rightarrow\mathrm{Hom}_{\mathcal C}(A,B)\rightarrow\mathrm{Hom}_{\mathcal C}(P(A),B),
and take the cohomology on the righthand side.

 

<< PreviousWord BrowserNext >>
higinio mornigo
upfield railway line, melbourne
battlefield 1918
robert morison
rocket j. squirrel
muhammad ii
karl philipp moritz
francesco morlacchi
charkha
puerto rican independence movement
involute
captain blackadder
james wilson morrice
charles morris (naval officer)
edward taylor
margaret iii of flanders
glenn morris
the great war (game)
michael morris, 1st baron killanin
m.i.u. album
sog
national youth service
hendrick antony kramers
roland sletor morris
john morris jones
leyton midland road railway station
rich kids on lsd (r.k.l.)
lord flashheart
de lesseps story morrison
pelagon
keepin' the summer alive (album)
who dares wins (game)
robert morrison
jedidiah morse
f. courty
sidney edwards morse
sharpitor
list of heads of state of ecuador
macdill air force base
botswana defence force air wing
tony conigliaro
edouard adolphe casimir joseph mortier
john parker (uk politician)
draft
Copyright 2005-2009 OnPedia.com. All Rights Reserved