Theorems · Definition · category theory
CategoryTheory.Core.functorToCore
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{G : Type u₂} →
[inst_1 : CategoryTheory.Groupoid G] →
CategoryTheory.Functor G C → CategoryTheory.Functor G (CategoryTheory.Core C)A functor from a groupoid to a category C factors through the core of C.
- Defined in
- Mathlib.CategoryTheory.Core
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Homproof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.Groupoidstatement and proof · cited by 182
- CategoryTheory.Corestatement · cited by 85
- CategoryTheory.Groupoid.invproof · cited by 36
Cited by12
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.coreproof · cited by 36
- CategoryTheory.Core.functorToCoreCompLeftIsostatement and proof · cited by 1
- CategoryTheory.Core.functorToCoreCompRightIsostatement and proof · cited by 1
- CategoryTheory.Core.functorToCoreInclusionIsostatement and proof · cited by 1
- CategoryTheory.Core.inclusionCompFunctorToCoreIsostatement and proof · cited by 1
- CategoryTheory.Core.functorToCore_comp_leftstatement and proof · cited by 0
- CategoryTheory.Core.functorToCore_comp_rightstatement and proof · cited by 0
- CategoryTheory.Core.functorToCore_inclusionstatement and proof · cited by 0
- CategoryTheory.Core.functorToCore_map_iso_homstatement and proof · cited by 0
- CategoryTheory.Core.functorToCore_map_iso_invstatement · cited by 0
- CategoryTheory.Core.functorToCore_obj_ofstatement and proof · cited by 0
- CategoryTheory.Core.inclusion_comp_functorToCorestatement and proof · cited by 0