Theorems · Definition · category theory
TopologicalSpace.Opens.toTopCat
(X : TopCat) → CategoryTheory.Functor (TopologicalSpace.Opens ↑X) TopCat
The functor from open sets in X to TopCat,
realising each open set as a topological space itself.
- Defined in
- Mathlib.Topology.Category.TopCat.Opens
- Cited by
- 81 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- TopCat.carrierstatement and proof · cited by 3,184
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- TopCatstatement and proof · cited by 1,889
- TopCat.ofHomproof · cited by 44
Cited by113
Results whose statement or proof uses this declaration.
- TopologicalSpace.Opens.inclusion'statement · cited by 73
- TopologicalSpace.Opens.isOpenEmbeddingstatement · cited by 49
- AlgebraicGeometry.Scheme.Opens.topIso_invstatement · cited by 15
- AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpecstatement · cited by 13
- TopCat.GlueData.ofOpenSubsetsproof · cited by 11
- AlgebraicGeometry.Scheme.Opens.topIso_homstatement · cited by 10
- AlgebraicGeometry.ProjIsoSpecTopComponent.toSpecstatement · cited by 9
- TopologicalSpace.OpenNhds.isOpenEmbeddingstatement · cited by 7
- AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.carrierstatement · cited by 5
- AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.mk_mem_carrierstatement · cited by 5
- AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓstatement · cited by 5
- TopCat.GlueData.MkCore.tstatement · cited by 4