Pushout of a module extension (source code)

= Pushout of a module extension
{title2=$B_f=(A\prime\oplus B)/\{(f(a),-i(a))\}$}

Pushing an inclusion $i:A\to B$ along $f:A\to A\prime$ gives a new <module extension> with kernel $A\prime$ and the same quotient. This <pushout> realizes the covariance of the degree-one <Ext functor> in its second argument.