Hom(''Z'', ''X'') -> Hom(''Z'', ''Y''), defined by 1=''f''_*(''h'') = ''f'' ? ''h'' for all morphisms ''h'' : ''Z'' -> ''X'', is injective for all objects Z.

Examples

Every morphism in a concrete category whose underlying function is injective is a monomorphism; in other words, if morphisms are actually functions between sets, then any morphism which is a one-to-one function will necessarily

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