2014-09-16 18:58:54 +00:00
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import algebra.category
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2014-09-14 19:01:14 +00:00
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open category
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inductive my_functor {obC obD : Type} (C : category obC) (D : category obD) : Type :=
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mk : Π (obF : obC → obD) (morF : Π{A B : obC}, mor A B → mor (obF A) (obF B)),
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(Π {A : obC}, morF (ID A) = ID (obF A)) →
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(Π {A B C : obC} {f : mor A B} {g : mor B C}, morF (g ∘ f) = morF g ∘ morF f) →
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my_functor C D
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definition my_object [coercion] {obC obD : Type} {C : category obC} {D : category obD} (F : my_functor C D) : obC → obD :=
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my_functor.rec (λ obF morF Hid Hcomp, obF) F
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definition my_morphism [coercion] {obC obD : Type} {C : category obC} {D : category obD} (F : my_functor C D) :
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Π{A B : obC}, mor A B → mor (my_object F A) (my_object F B) :=
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my_functor.rec (λ obF morF Hid Hcomp, morF) F
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variables obC obD : Type
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variables a b : obC
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variable C : category obC
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instance C
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variable D : category obD
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variable F : my_functor C D
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variable m : mor a b
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check F a
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check F m
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