diff --git a/theories/Homotopy/ClassifyingSpace.v b/theories/Homotopy/ClassifyingSpace.v index 20b8ffc532..d4cf92a1b3 100644 --- a/theories/Homotopy/ClassifyingSpace.v +++ b/theories/Homotopy/ClassifyingSpace.v @@ -581,7 +581,7 @@ Proof. rapply pequiv_pclassifyingspace_pi1. } snrapply Build_NatEquiv. 1: intro; exact pequiv_ptr_rec. - rapply is1natural_prewhisker. + rapply (is1natural_prewhisker (G:=opyon X) B (opyoneda _ _ _)). Defined. (** The classifying space functor and the fundamental group functor form an adjunction (pType needs to be restricted to the subcategory of 0-connected pTypes). Note that the full adjunction should also be natural in X, but this was not needed yet. *) diff --git a/theories/WildCat/Adjoint.v b/theories/WildCat/Adjoint.v index 9e44791f87..5e2800f613 100644 --- a/theories/WildCat/Adjoint.v +++ b/theories/WildCat/Adjoint.v @@ -376,7 +376,7 @@ Proof. exact (natequiv_prewhisker (A:=A^op) (B:=B^op) (natequiv_adjunction_l adj2 y) F). } intros x. - rapply is1natural_comp. + nrapply is1natural_comp. + rapply (is1natural_prewhisker G' (natequiv_adjunction_r adj1 x)). + rapply is1natural_equiv_adjunction_r. Defined. @@ -393,7 +393,7 @@ Proof. refine (natequiv_compose (natequiv_adjunction_l adj _) _). rapply (natequiv_postwhisker _ (natequiv_op e)). } intros x. - rapply is1natural_comp. + nrapply is1natural_comp; typeclasses eauto. Defined. (** Replace the right functor in an adjunction by a naturally equivalent one. *) @@ -408,8 +408,7 @@ Proof. refine (natequiv_compose _ (natequiv_adjunction_r adj _)). rapply (natequiv_postwhisker _ e). } intros y. - rapply is1natural_comp. + nrapply is1natural_comp. 2: exact _. rapply is1natural_yoneda. Defined. - diff --git a/theories/WildCat/NatTrans.v b/theories/WildCat/NatTrans.v index ce2871fa1e..eb47b3c164 100644 --- a/theories/WildCat/NatTrans.v +++ b/theories/WildCat/NatTrans.v @@ -66,7 +66,7 @@ Arguments Is1Natural {A B} {isgraph_A} F {is0functor_F} G {is0functor_G} alpha : rename. Arguments isnat {_ _ _ _ _ _ _ _ _ _ _} alpha {alnat _ _} f : rename. Arguments isnat_tr {_ _ _ _ _ _ _ _ _ _ _} alpha {alnat _ _} f : rename. - +Hint Mode Is1Natural - - - - - - - - - - - ! : typeclass_instances. (** We coerce naturality proofs to their naturality square as the [isnat] projection can be unwieldy in certain situations where the transformation is difficult to write down. This allows for the naturality proof to be used directly. *) Coercion isnat : Is1Natural >-> Funclass.