CatDat

zero morphisms

A category has zero morphisms if for every pair of objects A,BA,B there is a distinugished morphism 0A,B:AB0_{A,B} : A \to B, called the zero morphism, such that we have f0A,B=0A,Cf \circ 0_{A,B} = 0_{A,C} and 0B,Cg=0A,C0_{B,C} \circ g = 0_{A,C} for all morphisms f:BCf : B \to C and g:ABg : A \to B. The zero morphisms are unique if they exist, hence this is actually a property of the category.

Relevant implications

Examples

Counterexamples

Unknown

For these categories the database has no info if they satisfy this property or not.