Theorems · Theorem · category theory
CategoryTheory.Subfunctor.mem_ofSection_obj
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {F : CategoryTheory.Functor Cᵒᵖ (Type w)} {X : Cᵒᵖ}
(x : F.obj X), x ∈ (CategoryTheory.Subfunctor.ofSection x).obj X- Cited by
- 3 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, 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.
- Setstatement · cited by 53,352
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- CategoryTheory.Functor.map_idproof · cited by 616
- CategoryTheory.Subfunctor.objstatement · cited by 227
- CategoryTheory.types_congr_homproof · cited by 149
- CategoryTheory.id_applyproof · cited by 100
- CategoryTheory.Subfunctor.ofSectionstatement · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- SSet.Subcomplex.mem_ofSimplex_objproof · cited by 5
- CategoryTheory.Subfunctor.ofSection_le_iffproof · cited by 4
- CategoryTheory.Subfunctor.ofSection_imageproof · cited by 1