CatDat

constant

A morphism $f : A \to B$ is called constant if for all morphisms $a_1,a_2 : T \rightrightarrows A$ we have $f \circ a_1 = f \circ a_2$. This is a categorical generalization of the concept of a constant function.

• Dual property: coconstant
• nLab Link

Relevant implications

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

Examples

There are 6 morphisms with this property.

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

Counterexamples

There are 9 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
• 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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