mathlib documentation

algebra.category.Group.images

The category of commutative additive groups has images. #

Note that we don't need to register any of the constructions here as instances, because we get them from the fact that AddCommGroup is an abelian category.

def AddCommGroup.image {G H : AddCommGroup} (f : G H) :

the image of a morphism in AddCommGroup is just the bundling of add_monoid_hom.range f

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the inclusion of image f into the target

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the corestriction map to the image

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the universal property for the image factorisation

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the factorisation of any morphism in AddCommGroup through a mono.

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the factorisation of any morphism in AddCommGroup through a mono has the universal property of the image.

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The categorical image of a morphism in AddCommGroup agrees with the usual group-theoretical range.

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