Theorems · Theorem · category theory

CategoryTheory.Subobject.inf_map

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Limits.HasPullbacks C] {X Y : C}
  (g : Y ⟶ X) [inst_2 : CategoryTheory.Mono g] (f₁ f₂ : CategoryTheory.Subobject Y),
  (CategoryTheory.Subobject.map g).obj (f₁ ⊓ f₂) =
    (CategoryTheory.Subobject.map g).obj f₁ ⊓ (CategoryTheory.Subobject.map g).obj f₂

⊓ commutes with map.

Defined in

Mathlib.CategoryTheory.Subobject.Lattice

Cited by

0 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacksCategoryTheory.Mono