overEquiv_top — Mathlib

English

Several lemmas state the behavior of overEquiv with respect to top and pullback/pushforward operations.

Русский

Несколько лемм описывают поведение overEquiv относительно верхнего севея и операций подстановки/перемещения.

LaTeX

$$$$ \text{(typical identities involving top, pullback, pushforward and forgetful functor)} $$$$

Lean4

@[simp]
theorem overEquiv_top {X : C} (Y : Over X) : overEquiv Y ⊤ = ⊤ :=
  by
  ext Z g
  simp only [top_apply, iff_true]
  dsimp [overEquiv, Presieve.functorPushforward]
  exact ⟨Y, 𝟙 Y, g, by simp, by simp⟩

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