compRight — Mathlib

English

Proofs about eq of compLeft function constructions, ensuring coherence of the functorial structure.

Русский

Доказательства равенств конструкций compLeft, обеспечивающих согласованность функторной структуры.

LaTeX

$$$\mathrm{compLeft}\;\text{eq}_1 = \mathrm{eq}_1$$$

Lean4

/-- `ContinuousMonoidHom f _` is a functor. -/
@[to_additive /-- `ContinuousAddMonoidHom f _` is a functor. -/
    ]
def compRight {B : Type*} [CommGroup B] [TopologicalSpace B] [IsTopologicalGroup B] (f : ContinuousMonoidHom B E) :
    ContinuousMonoidHom (ContinuousMonoidHom A B) (ContinuousMonoidHom A E)
    where
  toFun g := f.comp g
  map_one' := ext fun _a => map_one f
  map_mul' g h := ext fun a => map_mul f (g a) (h a)
  continuous_toFun := f.continuous_comp_right

Похожие утверждения