Theorems · Inductive type · category theory
CategoryTheory.InducedCategory.Hom
{C : Type u₁} →
{D : Type u₂} →
[CategoryTheory.Category.{v, u₂} D] →
{F : C → D} → CategoryTheory.InducedCategory D F → CategoryTheory.InducedCategory D F → Type vThe type of morphisms in InducedCategory D F between X and Y
is a 1-field structure which identifies to F X ⟶ F Y.
- Defined in
- Mathlib.CategoryTheory.InducedCategory
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 1 from the axioms · 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.InducedCategorystatement · cited by 71
Cited by19
Results whose statement or proof uses this declaration.
- CategoryTheory.InducedCategory.Hom.homstatement and proof · cited by 850
- CategoryTheory.InducedCategory.Hom.casesOnstatement and proof · cited by 2
- CategoryTheory.InducedCategory.Hom.extstatement and proof · cited by 2
- CategoryTheory.InducedCategory.comp_homstatement and proof · cited by 2
- TannakaDuality.FiniteGroup.toRightFDRepComp_in_rightRegularproof · cited by 1
- TannakaDuality.FiniteGroup.toRightFDRepComp_injectiveproof · cited by 1
- AlgebraicGeometry.SheafedSpace.epi_of_base_surjective_of_stalk_monoproof · cited by 1
- CategoryTheory.InducedCategory.Hom.mk.injstatement · cited by 1
- CategoryTheory.InducedCategory.Hom.mk.noConfusionstatement · cited by 1
- AlgebraicGeometry.SheafedSpace.mono_of_base_injective_of_stalk_epiproof · cited by 1
- CategoryTheory.InducedCategory.Hom.ctorIdxstatement and proof · cited by 0
- CategoryTheory.InducedCategory.Hom.ext_iffstatement and proof · cited by 0