Theorems · Inductive type · category theory
CategoryTheory.Subfunctor
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.Functor C (Type w) → Type (max u w)A subfunctor of a functor consists of a subset of F.obj U for every U,
compatible with the restriction maps F.map i.
- Defined in
- Mathlib.CategoryTheory.Subfunctor.Basic
- Cited by
- 112 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 51 definitions · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.Functorstatement · cited by 16,252
Cited by152
Results whose statement or proof uses this declaration.
- SSet.Subcomplexproof · cited by 461
- CategoryTheory.Subfunctor.objstatement and proof · cited by 227
- CategoryTheory.Subfunctor.toFunctorstatement and proof · cited by 90
- CategoryTheory.Subfunctor.ιstatement and proof · cited by 50
- CategoryTheory.Subfunctor.rangestatement · cited by 46
- CategoryTheory.Subfunctor.extstatement and proof · cited by 38
- CategoryTheory.Subfunctor.iSup_objstatement and proof · cited by 23
- CategoryTheory.Subfunctor.equalizerstatement and proof · cited by 17
- CategoryTheory.Subfunctor.sheafifystatement and proof · cited by 16
- CategoryTheory.Subfunctor.ofSectionstatement · cited by 14
- CategoryTheory.Sieve.shrinkFunctorstatement · cited by 14
- CategoryTheory.Subfunctor.IsGeneratedBystatement and proof · cited by 11