Theorems · Definition · category theory

CategoryTheory.MonoOver.mapBot

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {X Y : C} →
      [inst_1 : CategoryTheory.Limits.HasInitial C] →
        [inst_2 : CategoryTheory.Limits.InitialMonoClass C] →
          (f : X ⟶ Y) → [inst_3 : CategoryTheory.Mono f] → (CategoryTheory.MonoOver.map f).obj ⊥ ≅ ⊥

map f sends ⊥ : MonoOver X to ⊥ : MonoOver Y.

Defined in

Mathlib.CategoryTheory.Subobject.Lattice

Cited by

1 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasInitialCategoryTheory.Limits.InitialMonoClassCategoryTheory.Mono