Is this the definition of an exact sequence in an Abelian category: $A\xrightarrow{f}B\xrightarrow{g}C$ is exact at $B$ if $ker(g)=im(f)$?
That what it says at the start of page 7 in Weible.
Why does this comment (Weibel IHA Exercise 1.2.4) say otherwise, can someone provide a reference?