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feat(category/has_shift): missing simp lemmas (#3365)
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Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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semorrison and semorrison committed Jul 11, 2020
1 parent f669a78 commit 75b9cfa
Showing 1 changed file with 10 additions and 1 deletion.
11 changes: 10 additions & 1 deletion src/category_theory/graded_object.lean
Expand Up @@ -125,13 +125,22 @@ def comap_equiv {β γ : Type w} (e : β ≃ γ) :

end

instance has_shift {β : Type} [add_comm_group β] (s : β) : has_shift (graded_object_with_shift s C) :=
instance has_shift {β : Type*} [add_comm_group β] (s : β) : has_shift (graded_object_with_shift s C) :=
{ shift := comap_equiv C
{ to_fun := λ b, b-s,
inv_fun := λ b, b+s,
left_inv := λ x, (by simp),
right_inv := λ x, (by simp), } }

@[simp] lemma shift_functor_obj_apply {β : Type*} [add_comm_group β] (s : β) (X : β → C) (t : β) :
(shift (graded_object_with_shift s C)).functor.obj X t = X (t + s) :=
rfl

@[simp] lemma shift_functor_map_apply {β : Type*} [add_comm_group β] (s : β)
{X Y : graded_object_with_shift s C} (f : X ⟶ Y) (t : β) :
(shift (graded_object_with_shift s C)).functor.map f t = f (t + s) :=
rfl

instance has_zero_morphisms [has_zero_morphisms C] (β : Type w) :
has_zero_morphisms.{(max w v)} (graded_object β C) :=
{ has_zero := λ X Y,
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