Left-exact reflective subcategory of a regular category
ID: left-exact-reflective-subcategory-of-a-regular-category
Every left-exact reflective subcategory of a regular category is regular. The reflector sends a regular-epimorphism--monomorphism factorization to such a factorization among fixed objects. A morphism between fixed objects is a regular epimorphism precisely when the closure of its image under the closure operation induced by a left-exact reflector is the whole codomain; pullback stability follows from pullback stability of images and of closure.
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