= Homotopy retract
{title2=$ri=\operatorname{id}_A,\ ir\simeq\operatorname{id}_X$}
In the Oxford course's convention, a <homotopy retract> is a <retraction> $r:X\to A$ such that the <inclusion map> $i:A\hookrightarrow X$ also satisfies $ir\simeq\operatorname{id}_X$. It gives a <homotopy equivalence> between $A$ and $X$. Unlike the <deformation retraction> convention used here, the <homotopy> need not fix $A$ at intermediate times. https://people.maths.ox.ac.uk/lackenby/tg11o17.pdf#page=16[Topology and Groups, Definition II.11, printed p. 16]{ref}
Back to article page
