Theorems · Definition · category theory

CategoryTheory.Subobject.underlyingIso

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {X Y : C} →
      (f : X ⟶ Y) →
        [inst_1 : CategoryTheory.Mono f] → CategoryTheory.Subobject.underlying.obj (CategoryTheory.Subobject.mk f) ≅ X

If we construct a Subobject Y from an explicit f : X ⟶ Y with [Mono f], then pick an arbitrary choice of underlying object (Subobject.mk f : C) back in C, it is isomorphic (in C) to the original X.

Defined in

Mathlib.CategoryTheory.Subobject.Basic

Cited by

41 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Mono