Theorems · Definition · category theory
TopCat.Hom.hom
{X Y : TopCat} → X.Hom Y → C(↑X, ↑Y)Turn a morphism in TopCat back into a ContinuousMap.
- Defined in
- Mathlib.Topology.Category.TopCat.Basic
- Cited by
- 169 results in Mathlib
- Foundations
- Depth 21 from the axioms, rests on 84 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierstatement · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- TopCatstatement and proof · cited by 1,889
- TopCat.Homstatement and proof · cited by 3
Cited by200
Results whose statement or proof uses this declaration.
- TopCat.isEmbeddingproof · cited by 67
- AlgebraicGeometry.Scheme.Hom.continuousproof · cited by 41
- AlgebraicGeometry.Scheme.Hom.comp_applyproof · cited by 32
- FundamentalGroupoid.fundamentalGroupoidFunctorproof · cited by 21
- TopCat.Homotopyproof · cited by 18
- AlgebraicGeometry.Scheme.fromSpecResidueField_applyproof · cited by 14
- CompHausLike.LocallyConstant.functorToPresheavesproof · cited by 11
- AlgebraicGeometry.IsAffineOpen.range_fromSpecproof · cited by 8
- AlgebraicGeometry.Scheme.Hom.isAffineOpen_iff_of_isOpenImmersionproof · cited by 7
- TopCat.toSSetObj₁Equivproof · cited by 6
- topToPreordproof · cited by 5
- CompHausLike.effectiveEpiStructproof · cited by 5