Are section and retraction dual properties?

Question

We know that being epic and being monic are dual to each other. Is being section/retraction also dual to being retraction/section?

Answer 1

Another term for section and retraction is split mono and split epi. At any rate, if $r\circ s = id$ then $s \circ^{op} r = id$ in the opposite category, so, yes, they are dual.

Answer 2

Well, it depends on precisely what you mean.

Yes, they are dual. Given $g:Y \to X$ and $f:X \to Y$, we have that $f$ being a retract to $g$, is equivalent to saying that $f \circ g =id$, whereas, reversing the arrows, $f$ is a section of $g$ if and only if $g \circ f=id$