An image of is the least subobject through which factors. In a category with pullback in a category constructions this gives a strong epimorphism–monomorphism factorization : pull back any mono in a lifting square for to ; minimality of the image forces the resulting mono to be invertible, producing a diagonal. Conversely, the lifting property of the strong part proves minimality. No stability under pullback is asserted; that is an additional property in a regular category.
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