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Simplify two definitions
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jwiegley committed Jan 30, 2024
1 parent 9a17d8b commit 5336ee1
Showing 1 changed file with 2 additions and 16 deletions.
18 changes: 2 additions & 16 deletions Theory/Kan/Extension.v
Original file line number Diff line number Diff line change
Expand Up @@ -54,15 +54,8 @@ Class LocalRightKan (X : A ⟶ C) := {
#[export] Program Instance RightKan_to_LocalRightKan {R : RightKan} (X : A ⟶ C) :
LocalRightKan X := {|
LocalRan := Ran X;
ran_transform :=
let adj_from := from (@adj _ _ _ _ ran_adjoint (Ran X) X) nat_id in
{| transform := transform[adj_from]
; naturality := naturality[adj_from] |}
ran_transform := from (@adj _ _ _ _ ran_adjoint (Ran X) X) nat_id
|}.
Next Obligation.
srewrite_r (naturality[from (@adj _ _ _ _ ran_adjoint (Ran X) X) nat_id]).
reflexivity.
Qed.
Next Obligation.
exists (to (@adj _ _ _ _ (@ran_adjoint R) M X) μ).
- intros.
Expand Down Expand Up @@ -112,15 +105,8 @@ Class LocalLeftKan (X : A ⟶ C) := {
#[export] Program Instance LeftKan_to_LocalLeftKan {R : LeftKan} (X : A ⟶ C) :
LocalLeftKan X := {|
LocalLan := Lan X;
lan_transform :=
let adj_to := to (@adj _ _ _ _ lan_adjoint X (Lan X)) nat_id in
{| transform := transform[adj_to]
; naturality := naturality[adj_to] |}
lan_transform := to (@adj _ _ _ _ lan_adjoint X (Lan X)) nat_id
|}.
Next Obligation.
srewrite_r (naturality[to (@adj _ _ _ _ lan_adjoint X (Lan X)) nat_id]).
reflexivity.
Qed.
Next Obligation.
exists (from (@adj _ _ _ _ (@lan_adjoint R) X M) ε).
- intros.
Expand Down

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