Theorems · Theorem · category theory
CategoryTheory.Subobject.ofLE_arrow
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {B : C} {X Y : CategoryTheory.Subobject B} (h : X ≤ Y),
CategoryTheory.CategoryStruct.comp (X.ofLE Y h) Y.arrow = X.arrow- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 39 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.
Cites10
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 · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.Subobject.underlyingstatement · cited by 211
- CategoryTheory.Subobject.arrowstatement · cited by 175
- CategoryTheory.Subobject.ofLEstatement · cited by 38
- LE.le.homproof · cited by 30
- CategoryTheory.Subobject.underlying_arrowproof · cited by 3
Cited by23
Results whose statement or proof uses this declaration.
- imageToKernel_arrowproof · cited by 15
- CategoryTheory.Subobject.ofMkLEMk_compproof · cited by 7
- CategoryTheory.Subobject.factors_of_leproof · cited by 5
- CategoryTheory.Subobject.inf_arrow_factors_leftproof · cited by 1
- CategoryTheory.Subobject.inf_arrow_factors_rightproof · cited by 1
- CategoryTheory.Subobject.inf_comp_leftproof · cited by 1
- CategoryTheory.Subobject.inf_comp_rightproof · cited by 1
- CategoryTheory.Subobject.inf_isPullbackproof · cited by 1
- CategoryTheory.Subobject.eq_of_le_of_isDetectingproof · cited by 1
- CategoryTheory.Subobject.ofLEMk_compproof · cited by 1
- imageToKernel_comp_rightproof · cited by 0