Theorems · Theorem · category theory
CategoryTheory.Over.mapId_eq
∀ {T : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} T] (Y : T),
CategoryTheory.Over.map (CategoryTheory.CategoryStruct.id Y) = CategoryTheory.Functor.id (CategoryTheory.Over Y)Mapping by the identity morphism is just the identity functor.
- Defined in
- Mathlib.CategoryTheory.Comma.Over.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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Cites15
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.Functorstatement · cited by 16,252
- CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
- CategoryTheory.Functor.idstatement · cited by 3,333
- CategoryTheory.Category.comp_idproof · cited by 2,119
- CategoryTheory.Overstatement and proof · cited by 935
- CategoryTheory.Comma.leftproof · cited by 886
- CategoryTheory.Comma.rightproof · cited by 727
- CategoryTheory.Over.leftproof · cited by 541
- CategoryTheory.Comma.homproof · cited by 490
- CategoryTheory.Over.mapstatement · cited by 97
- CategoryTheory.Functor.ext_of_isoproof · cited by 28
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