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In the category of sets objects are sets, morphisms are total functions, and a morphism composition is a function composition.
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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.
In the category of sets, the monomorphism is the injective function.
Commutative diagram for monomorphism m and two morphisms f and g.
In the category of sets, the isomorphism is the bijective function.
Commutative diagram for isomorphism f.
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.
Commutative diagram.
In the category of sets, the product is the cartesian product.
The universal property.
Commutative diagram.
In the category of sets, the coproduct is the disjoint union.
The universal property.
Complement.