background image

Special morphisms

Let

f

be a morphism of a partially ordered dagger category.

f

is

monovalued

when

f

f

1

Dst

f

.

f

is

entirely defined

when

f

f

1

Src

f

.

f

is

injective

when

f

f

1

Src

f

.

f

is

surjective

when

f

f

1

Dst

f

.

It’s easy to show that this is a generalization of monovalued,
entirely defined, injective, and surjective binary relations as
morphisms of the category

Rel

.

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