# Category of sets

The full description is available here in Russian.

## Sample objects and morphisms

In the category of sets objects are sets, morphisms are total functions, and a morphism composition is a function composition.

Double click on object to show or hide its internal structure.

To fix the node position, drag it with the Ctrl key pressed.

## Epimorphism

In the category of sets, the epimorphism is the surjective function.

Commutative diagram for epimorphism e and two morphisms f and g.

The diagram commutes (f h = g h) but f != g, because h is not epimorphism.

## Monomorphism

In the category of sets, the monomorphism is the injective function.

Commutative diagram for monomorphism m and two morphisms f and g.

## Isomorphism

In the category of sets, the isomorphism is the bijective function.

Commutative diagram for isomorphism f.

## Terminal, initial and null object

In the category of sets, the terminal object is the singleton set.

There are exists non-unique morphisms with a terminal object domain.

In the category of sets, the initial object is the empty set.

## Product

Commutative diagram.

In the category of sets, the product is the cartesian product.

The universal property.

## Coproduct

Commutative diagram.

In the category of sets, the coproduct is the disjoint union.

The universal property.

Complement.

## Equalizer

## Coequalizer

## Pullback

## Pushout