Theorems · Theorem · category theory
CategoryTheory.Subfunctor.range_obj
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {F F' : CategoryTheory.Functor C (Type w)} (p : F' ⟶ F)
(U : C), (CategoryTheory.Subfunctor.range p).obj U = Set.range ⇑(CategoryTheory.ConcreteCategory.hom (p.app U))- Defined in
- Mathlib.CategoryTheory.Subfunctor.Image
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 23 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.NatTrans.appstatement · cited by 7,406
- Set.rangestatement · cited by 4,705
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TypeCat.Funstatement · cited by 1,307
- CategoryTheory.Subfunctor.objstatement and proof · cited by 227
- CategoryTheory.Subfunctor.rangestatement and proof · cited by 46
Cited by14
Results whose statement or proof uses this declaration.
- SSet.iSup_range_eq_top_of_isColimitproof · cited by 3
- SSet.Subcomplex.image_topproof · cited by 2
- SSet.skeletonOfMono_succproof · cited by 1
- CategoryTheory.Subfunctor.range_le_equalizer_iffproof · cited by 1
- CategoryTheory.Subfunctor.epi_iff_range_eq_topproof · cited by 1
- CategoryTheory.Subfunctor.ofSection_eq_rangeproof · cited by 1
- CategoryTheory.Subfunctor.image_topproof · cited by 1
- SSet.Subcomplex.range_compproof · cited by 1
- SSet.Subcomplex.range_eq_top_iffproof · cited by 1
- SSet.relativeCellComplexOfMono.Cell.mem_skeletonOfMono_obj_iffproof · cited by 0
- CategoryTheory.Subfunctor.range_compproof · cited by 0
- CategoryTheory.Subfunctor.range_comp_leproof · cited by 0