Talk:Essential extension
Latest comment: 2 years ago by Hazelmaye in topic Essential extensions in general categories
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Essential extensions in general categories edit
Let C be a category. A morphism f: X → Y in C is essential if a morphism g: Y → Z is a monomorphism if and only if g ° f is a monomorphism. Taking g to be the identity morphism of Y shows that an essential morphism f must be a monomorphism.
If X has an injective envelope Y, then Y is the largest essential extension of X. But the largest essential extension may not be injective.
Hazelmaye (talk) 15:23, 18 June 2021 (UTC)[1]
References
- ^ Porst, Hans-E. (1981). "Characterization of injective envelopes". Cahiers de topologie et geometrie differentielle categoriques. 22 (4): 399–406.