CatDat

zero morphism

A morphism in an arbitrary category is a zero morphism if it is constant and coconstant. In a category with zero morphisms, for every pair of objects $A,B$, there is a unique morphism $A \to B$ with this property, the distinguished zero morphism $0_{A,B} : A \to B$ (see here).

• Dual property: zero morphism (self-dual)
• Related properties: coconstant, constant
• nLab Link

Relevant implications

• coconstant andconstant is equivalent to zero morphism
• coconstant () implies zero morphism
• constant () implies zero morphism

Examples

There are 5 morphisms with this property.

• example of a non-strong extremal monomorphism
• handle of the universal fork
• map from the empty set
• universal morphism
• universal split epimorphism

Counterexamples

There are 10 morphisms without this property.

• Baer-Specker relations
• embedding of A3 into S3
• embedding of integer into rational numbers
• identity map of a group
• identity map of a set
• inclusion of positive numbers
• map into the singleton set
• multiplication with 2
• presentation of the walking idempotent
• reduction modulo p

Unknown

There are 0 morphisms for which the database has no information on whether they satisfy this property.

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