Theorems · Definition · category theory
CategoryTheory.Subfunctor.toRange
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{F F' : CategoryTheory.Functor C (Type w)} → (p : F' ⟶ F) → F' ⟶ (CategoryTheory.Subfunctor.range p).toFunctorGiven a morphism p : F' ⟶ F of type-valued functors, this is the morphism
from F' to its range.
- Defined in
- Mathlib.CategoryTheory.Subfunctor.Image
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 63 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.
Cites6
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.Functorstatement and proof · cited by 16,252
- CategoryTheory.Subfunctor.toFunctorstatement · cited by 90
- CategoryTheory.Subfunctor.rangestatement · cited by 46
- CategoryTheory.Subfunctor.liftproof · cited by 9
Cited by15
Results whose statement or proof uses this declaration.
- CategoryTheory.Subfunctor.equivalenceMonoOverproof · cited by 8
- SSet.Subcomplex.toRangeproof · cited by 6
- CategoryTheory.Subfunctor.toRange_ιstatement · cited by 3
- CategoryTheory.FunctorToTypes.monoFactorisationproof · cited by 3
- CategoryTheory.Sheaf.toImage_ιproof · cited by 2
- CategoryTheory.Subfunctor.toRangeSheafifyproof · cited by 2
- CategoryTheory.FunctorToTypes.monoFactorisation_estatement · cited by 0
- CategoryTheory.Subfunctor.equivalenceMonoOver_counitIsostatement · cited by 0
- CategoryTheory.imageFactorizationproof · cited by 0
- CategoryTheory.Subfunctor.range_toRangestatement and proof · cited by 0
- SSet.strongAnodyneExtensions_le_anodyneExtensionsproof · cited by 0
- CategoryTheory.Subfunctor.toRangeSheafify_app_hom_apply_coestatement · cited by 0