**Zero Morphisms**

A **zero morphism** in a category is a generalised absorbing element under function composition: any morphism composed with a zero morphism gives a zero morphism. Specifically, if 0_{XY} : *X* → *Y* is the zero morphism among morphisms from *X* to *Y*, and *f* : *A* → *X* and *g* : *Y* → *B* are arbitrary morphisms, then *g* ∘ 0_{XY} = 0_{XB} and 0_{XY} ∘ *f* = 0_{AY}.

If a category has a zero object **0**, then there are canonical morphisms *X* → **0** and **0** → *Y*, and composing them gives a zero morphism 0_{XY} : *X* → *Y*. In the category of groups, for example, zero morphisms are morphisms which always return group identities, thus generalising the function *z*(*x*) = 0.

Read more about this topic: List Of Zero Terms

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