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Wildcat rewriting tweaks #2208

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Wildcat rewriting tweaks #2208

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patrick-nicodemus Jan 21, 2025
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patrick-nicodemus Jan 21, 2025
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Made a change to Hint Mode
patrick-nicodemus Jan 24, 2025
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Merge branch 'master' into wildcat-rewriting-tweaks
patrick-nicodemus Jan 24, 2025
c7a44fa
Fixed broken proof
patrick-nicodemus Jan 24, 2025
0ea00ce
Removed accidental code
patrick-nicodemus Jan 26, 2025
cf3f88e
Removed accidental code
patrick-nicodemus Jan 26, 2025
9861b77
Update theories/Homotopy/ClassifyingSpace.v
patrick-nicodemus Jan 27, 2025
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3 changes: 2 additions & 1 deletion theories/Homotopy/ClassifyingSpace.v
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Expand Up @@ -581,7 +581,8 @@ Proof.
rapply pequiv_pclassifyingspace_pi1. }
snrapply Build_NatEquiv.
1: intro; exact pequiv_ptr_rec.
rapply is1natural_prewhisker.
rapply (@is1natural_prewhisker _ _ _
(opyon (pTr 1 X)) (opyon X) B _ _ _ _ _ _ _ _ _ _ (opyoneda _ _ _)).
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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. *)
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7 changes: 3 additions & 4 deletions theories/WildCat/Adjoint.v
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Expand Up @@ -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.
Expand All @@ -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. *)
Expand All @@ -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.

2 changes: 1 addition & 1 deletion theories/WildCat/NatTrans.v
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Expand Up @@ -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.

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