Theorems · Theorem · category theory
CategoryTheory.Subobject.map_id
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} (x : CategoryTheory.Subobject X),
(CategoryTheory.Subobject.map (CategoryTheory.CategoryStruct.id X)).obj x = x- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.CategoryStruct.idstatement · cited by 6,235
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.Iso.appproof · cited by 253
- CategoryTheory.MonoOverproof · cited by 115
- Quotient.inductionOn'proof · cited by 69
- CategoryTheory.Subobject.mapstatement · cited by 19
- CategoryTheory.MonoOver.mapIdproof · cited by 3
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