List of Zero Terms - Zero Morphisms

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 0XY : XY is the zero morphism among morphisms from X to Y, and f : AX and g : YB are arbitrary morphisms, then g ∘ 0XY = 0XB and 0XYf = 0AY.

If a category has a zero object 0, then there are canonical morphisms X0 and 0Y, and composing them gives a zero morphism 0XY : XY. In the category of groups, for example, zero morphisms are morphisms which always return group identities, thus generalising the function z(x) = 0.

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