@Igor – I think that's a good rule-of-thumb but there are some gotchas to bear in mind.

• talking about \\(f\\) being "injective" or "surjective" only makes sense in categories where the arrows are functions of some sort

• any function with a left inverse is injective, but not vice versa – consider the map \\(\varnothing \rightarrow \textrm{1}\\)

• any function with a right inverse is surjective, but the converse only holds if we have the Axiom of Choice

• talking about \\(f\\) being "injective" or "surjective" only makes sense in categories where the arrows are functions of some sort

• any function with a left inverse is injective, but not vice versa – consider the map \\(\varnothing \rightarrow \textrm{1}\\)

• any function with a right inverse is surjective, but the converse only holds if we have the Axiom of Choice