2014-10-09 06:44:09 +00:00
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import algebra.category.basic
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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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2014-10-09 06:44:09 +00:00
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mk : Π (obF : obC → obD) (homF : Π{A B : obC}, hom A B → hom (obF A) (obF B)),
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(Π {A : obC}, homF (ID A) = ID (obF A)) →
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(Π {A B C : obC} {f : hom A B} {g : hom B C}, homF (g ∘ f) = homF g ∘ homF f) →
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2014-09-14 19:01:14 +00:00
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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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2014-10-09 06:44:09 +00:00
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my_functor.rec (λ obF homF Hid Hcomp, obF) F
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2014-09-14 19:01:14 +00:00
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2014-10-09 06:44:09 +00:00
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definition my_homphism [coercion] {obC obD : Type} {C : category obC} {D : category obD} (F : my_functor C D) :
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Π{A B : obC}, hom A B → hom (my_object F A) (my_object F B) :=
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my_functor.rec (λ obF homF Hid Hcomp, homF) F
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2014-09-14 19:01:14 +00:00
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2014-10-02 23:20:52 +00:00
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constants obC obD : Type
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constants a b : obC
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constant C : category obC
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2014-09-14 19:01:14 +00:00
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instance C
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2014-10-02 23:20:52 +00:00
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constant D : category obD
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constant F : my_functor C D
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2014-10-09 06:44:09 +00:00
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constant m : hom a b
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2014-09-14 19:01:14 +00:00
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check F a
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check F m
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