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Adjust pmap_(pre/post)whisker in pHomotopy.v
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jdchristensen committed Dec 30, 2023
1 parent 8b57d0b commit e995adb
Showing 1 changed file with 8 additions and 6 deletions.
14 changes: 8 additions & 6 deletions theories/Pointed/pHomotopy.v
Original file line number Diff line number Diff line change
Expand Up @@ -25,16 +25,18 @@ Defined.

(** ** Whiskering of pointed homotopies by pointed functions *)

Definition pmap_postwhisker {A B C : pType} {f g : A $-> B}
(h : B $-> C) (p : f ==* g) : h o* f ==* h o* g.
Definition pmap_postwhisker {A : pType@{u1}} {B : pType@{u2}} {C : pType@{u3}}
{f g : A ->* B} (h : B ->* C) (p : f ==* g)
: h o* f ==* h o* g.
Proof.
exact (h $@L p).
exact (cat_postwhisker (A:=pType@{v}) h p).
Defined.

Definition pmap_prewhisker {A B C : pType} (f : A $-> B)
{g h : B $-> C} (p : g $== h) : g o* f ==* h o* f.
Definition pmap_prewhisker {A : pType@{u1}} {B : pType@{u2}} {C : pType@{u3}}
(f : A ->* B) {g h : B ->* C} (p : g $== h)
: g o* f ==* h o* f.
Proof.
exact (p $@R f).
exact (cat_prewhisker (A:=pType@{v}) p f).
Defined.

(** ** [phomotopy_path] respects 2-cells. *)
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