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Let C be the category with all equalizers, and let F: C → D be the conservative functor that keeps equalizers. Show that F is also the right functor.
Definitions:
The right functor is F: C → D, which is called a right functor if its action on morphisms is differentiated between certain objects. f. For any objects A, B in category C and morphisms f, g: A → B, if F f = F g, then f = g.
Functor F: C → D is a conservative functor if it reflects isomorphisms, etc. E. For any objects A, B in category C and morphism f: A → B, if F f is isomorphism, then f is also isomorphism.
Let C be the category with all equalizers, and let F: C → D be the conservative functor that keeps equalizers. Show that F is also the right functor.
Definitions:
The right functor is F: C → D, which is called a right functor if its action on morphisms is differentiated between certain objects. f. For any objects A, B in category C and morphisms f, g: A → B, if F f = F g, then f = g.
Functor F: C → D is a conservative functor if it reflects isomorphisms, etc. E. For any objects A, B in category C and morphism f: A → B, if F f is isomorphism, then f is also isomorphism.
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