map — Mathlib

English

In the opposite category, the inclusion object preserves the same underlying neighborhood structure under unop.

Русский

В противоположной категории включение сохраняет ту же самую структуру окрестности под unop.

LaTeX

$$inclusion_obj (x) (U) (p) : (inclusion x).obj ⟨U, p⟩ = U$$

Lean4

/-- The preimage functor from neighborhoods of `f x` to neighborhoods of `x`. -/
def map (x : X) : OpenNhds (f x) ⥤ OpenNhds x
    where
  obj U := ⟨(Opens.map f).obj U.1, U.2⟩
  map i := (Opens.map f).map i

Похожие утверждения