Let $ f{\colon}\linebreak[0] A \to B $ be a map in a category $ \mathscr{A} $ . A section (or right inverse) of $ f $ is a map $ i{\colon}\linebreak[0] B \to A $ in $ \mathscr{A} $ such that $ f \circ i = 1_B $ . In the category of sets, any map with a section is certainly surjective.