Everyday examples of morphisms with one-sided inverses

from blog The Universe of Disco, | ↗ original
Like almost everyone except Alexander Grothendieck, I understand things better with examples. For instance, how do you explain that $$(f\circ g)^{-1} = g^{-1} \circ f^{-1}?$$ Oh, that's easy. Let be putting on your shoes and be taking off your shoes. And let be putting on your socks and be taking off your socks. Now is putting on your...