CatDat

coconstant

A morphism $f : A \to B$ is called coconstant if for all morphisms $b_1,b_2 : B \rightrightarrows T$ we have $b_1 \circ f = b_2 \circ f$.

• Dual property: constant
• nLab Link

Relevant implications

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

Examples

There are 6 morphisms with this property.

• embedding of integer into rational numbers
• 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 9 morphisms without this property.

• Baer-Specker relations
• embedding of A3 into S3
• 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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