English
Equations about equality of left composition maps on opposite opens carrier
Русский
Эквивалентности левой композиции на носителях противоположных открытых множеств
LaTeX
$$eq_1 (IM I M G) (U) ...$$
Lean4
/-- The presheaf of smooth functions from `M` to `A`, for `A` an abelian Lie group, as a
presheaf of abelian groups. -/
@[to_additive /-- The presheaf of smooth functions from `M` to `A`, for `A` an additive abelian Lie
group, as a presheaf of additive abelian groups. -/
]
noncomputable def smoothPresheafCommGroup : TopCat.Presheaf CommGrpCat.{u} (TopCat.of M) :=
{ obj := fun U ↦ CommGrpCat.of ((smoothSheaf IM I M A).presheaf.obj U)
map := fun h ↦ CommGrpCat.ofHom <| ContMDiffMap.restrictMonoidHom IM I A <| CategoryTheory.leOfHom h.unop
map_id := fun _ ↦ rfl
map_comp := fun _ _ ↦ rfl }
