Theorems · Theorem · category theory
CategoryTheory.Over.homMk_left
∀ {T : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} T] {X : T} {U V : CategoryTheory.Over X} (f : U.left ⟶ V.left)
(w : autoParam (CategoryTheory.CategoryStruct.comp f V.hom = U.hom) CategoryTheory.Over.homMk._auto_1),
(CategoryTheory.Over.homMk f w).left = f- Defined in
- Mathlib.CategoryTheory.Comma.Over.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Functor.idstatement · cited by 3,333
- CategoryTheory.Discretestatement · cited by 2,447
- CategoryTheory.Overstatement and proof · cited by 935
- CategoryTheory.Functor.fromPUnitstatement · cited by 769
- CategoryTheory.Over.leftstatement and proof · cited by 541
- CategoryTheory.CommaMorphism.leftstatement and proof · cited by 526
- CategoryTheory.Over.homstatement and proof · cited by 370
- CategoryTheory.Over.homMkstatement and proof · cited by 115
Cited by12
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.pullbackMapproof · cited by 1
- CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_fstproof · cited by 1
- CategoryTheory.Over.μ_pullback_left_fst_fstproof · cited by 1
- CategoryTheory.Presieve.isSheafFor_over_map_op_comp_iffproof · cited by 1
- CategoryTheory.Over.μ_pullback_left_fst_sndproof · cited by 1
- CategoryTheory.CommSq.HasLift.overproof · cited by 1
- CategoryTheory.Over.prodComparisonIso_pullback_inv_left_fst_snd'proof · cited by 0
- CategoryTheory.Over.homMk_compproof · cited by 0
- CategoryTheory.Limits.diagonal_pullback_fstproof · cited by 0
- CategoryTheory.regularTopology.parallelPair_pullback_initialproof · cited by 0