# Morphism is a retraction of another morphism?

I have to use definition that morphism f is retraction of morphism g, but I don't know how to represent it. Any idea?

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Ah, this is related to your other question I just answered. The terminology isn't so good, because Hew's answer would be right most of the time, but in the context of model categories $f$ is a retraction of $g$ if it's a retract of $g$ in the category who objects are arrows in the original category $\mathcal{C}$ and whose morphisms are commutative squares. This is the diagram expressing the same information: $$\begin{matrix} A&\stackrel{i}{\to}&B&\stackrel{r}{\to}&A\\f\downarrow&&g\downarrow&&f\downarrow\\A'&\stackrel{j}{\longrightarrow}&B'&\stackrel{t}{\longrightarrow}&A'\end{matrix}$$ If $ri=1_A$ and $tj=1_{A'}$, we say $f$ is a retraction of $g.$
"$f$ is a retraction of $g$" probably just means that $fg = 1$ in your category, whatever that category is. I don't know what you mean by "how to represent it". What are you trying to do?