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t6s committed Jun 9, 2021
1 parent fa2b883 commit 5862948
Showing 1 changed file with 12 additions and 12 deletions.
24 changes: 12 additions & 12 deletions category_ext.v
Original file line number Diff line number Diff line change
Expand Up @@ -150,13 +150,13 @@ Section homfstsnd.
Let _homfst (x y : A * B) (f : {hom x,y}) : {hom x.1, y.1}.
case:f => f.
case/cid=> sf [] Hf _.
exact: (HomPack Hf).
exact: (HomPack _ _ _ Hf).
Defined.
Definition homfst := Eval hnf in _homfst.
Let _homsnd (x y : A * B) (f : {hom x,y}) : {hom x.2, y.2}.
case:f => f.
case/cid=> sf [] _ Hf.
exact: (HomPack Hf).
exact: (HomPack _ _ _ Hf).
Defined.
Definition homsnd := Eval hnf in _homsnd.
End homfstsnd.
Expand Down Expand Up @@ -242,7 +242,7 @@ exists (conj s1 s2); split.
rewrite (_ : h = g); first exact: Hom.class.
by rewrite boolp.funeqE => ?; rewrite /h /=; case: cid => ? [].
Qed.
Definition pairhom : {hom (a1, b1), (a2, b2)} := Hom.Pack _ pairhom'_in_hom.
Definition pairhom : {hom (a1, b1), (a2, b2)} := Hom.Pack _ _ pairhom'_in_hom.
End prodCat_pairhom.

Section pairhom_idfun.
Expand Down Expand Up @@ -296,7 +296,7 @@ End pairhomK.
Module papply_left.
Section def.
Variables A B C : category.
Variable F' : functor (productCategory A B) C.
Variable F' : {functor (productCategory A B) -> C}.
Variable a : A.
Definition F_obj : B -> C := fun b => F' (a, b).
Definition F_mor (b1 b2 : B) (f : {hom b1, b2}) : {hom F_obj b1, F_obj b2} :=
Expand All @@ -313,14 +313,14 @@ rewrite (_ : i = [hom (pairhom [hom idfun] g) \o
(pairhom [hom idfun] h)]) ?functor_o_hom //.
by apply/hom_ext => /=; rewrite boolp.funeqE; case.
Qed.
Definition F := Functor.Pack mixin_of.
Definition F := Functor.Pack (Phant _) mixin_of.
End def.
End papply_left.

Module papply_right.
Section def.
Variables A B C : category.
Variable F' : functor (productCategory A B) C.
Variable F' : {functor (productCategory A B) -> C}.
Variable b : B.
Definition F_obj : A -> C := fun a => F' (a, b).
Definition F_mor (a1 a2 : A) (f : {hom a1, a2}) : {hom F_obj a1, F_obj a2} :=
Expand All @@ -337,7 +337,7 @@ rewrite (_ : i = [hom (pairhom g [hom idfun]) \o
(pairhom h [hom idfun])]) ?functor_o_hom //.
by apply/hom_ext => /=; rewrite boolp.funeqE; case.
Qed.
Definition F := Functor.Pack mixin_of.
Definition F := Functor.Pack (Phant _) mixin_of.
End def.
End papply_right.

Expand All @@ -349,7 +349,7 @@ Module ProductFunctor.
*)
Section def.
Variables A1 B1 A2 B2 : category.
Variables (F1 : functor A1 B1) (F2 : functor A2 B2).
Variables (F1 : {functor A1 -> B1}) (F2 : {functor A2 -> B2}).
Local Notation A := (A1 * A2)%type.
Local Notation B := (B1 * B2)%type.
Definition acto (x : A) : B := pair (F1 x.1) (F2 x.2).
Expand All @@ -364,14 +364,14 @@ Next Obligation.
move=> [] a1 a2 [] b1 b2 [] c1 c2 g h.
by rewrite /actm homfst_comp homsnd_comp 2!functor_o_hom pairhom_comp.
Qed.
Definition F := Functor.Pack mixin_of.
Definition F := Functor.Pack (Phant _) mixin_of.
End def.
End ProductFunctor.

Module alpha_left.
Section alpha_left.
Variables A B C D : category.
Variable F' : functor (productCategory (productCategory A B) C) D.
Variable F' : {functor (productCategory (productCategory A B) C) -> D}.
Variables (a : A) (b : B).
Definition acto : C -> D := papply_left.F F' (a, b).
Definition actm (c1 c2 : C) (f : {hom c1, c2}) : {hom acto c1, acto c2} :=
Expand All @@ -388,7 +388,7 @@ rewrite (_ : i = [hom (pairhom [hom idfun] g) \o
(pairhom [hom idfun] h)]) ?functor_o_hom //.
by apply/hom_ext => /=; rewrite boolp.funeqE; case.
Qed.
Definition F : functor C D := Functor.Pack mixin_of.
Definition F : {functor C -> D} := Functor.Pack (Phant _) mixin_of.
End alpha_left.
End alpha_left.

Expand Down Expand Up @@ -462,6 +462,6 @@ Next Obligation.
case=> xa [] xb xc [] ya [] yb yc [] za [] zb zc g h.
by rewrite /actm !homsnd_comp !homfst_comp !pairhom_comp.
Qed.
Definition F := Functor.Pack mixin_of.
Definition F := Functor.Pack (Phant _) mixin_of.
End def.
End ProductCategoryAssoc.

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