Morphism

Monomorphism

A monomorphism is a left-cancellable morphism (denoted with ). A morphism is monic iff for any and cat

In a function is a monic iff it is injective iff it is left-invertible (i.e. split monic), but these are not equivalent in every concrete category, rather:

graph LR;
  left-invertible ==>|implies| injective ==>|implies| monic

Properties

See the dual properties.

1. If is monic then is monic.

Proof of 1

Note implies which holds iff , proving ^P1.

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