I am trying to find an example of a monomorphism that is not an injective map; much like there exist epimorphisms that are not surjective. Is this a bad question? Is every monomorphism defined on the category of sets injective? Any help would be great.
2026-05-06 06:11:19.1778047879
A monomorphism that is not injective
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Consider the category of pointed, connected, locally connected and locally path-connected spaces. Any nontrivial covering map is a monomorphism in this category which is not injective on underlying sets; this is a restatement of one of the lifting properties of covering maps.