Theorems · Definition · category theory
TopCat.isoOfHomeo
{X Y : TopCat} → ↑X ≃ₜ ↑Y → (X ≅ Y)Any homeomorphisms induces an isomorphism in Top.
- Defined in
- Mathlib.Topology.Category.TopCat.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Isostatement · cited by 3,963
- TopCat.carrierstatement and proof · cited by 3,184
- TopCatstatement and proof · cited by 1,889
- Homeomorphstatement and proof · cited by 725
- Homeomorph.symmproof · cited by 365
- toContinuousMapproof · cited by 99
- TopCat.ofHomproof · cited by 44
Cited by17
Results whose statement or proof uses this declaration.
- CompHausLike.isoOfHomeoproof · cited by 3
- ContinuousGeneratedByCat.equivalenceUnitIsoproof · cited by 1
- SSet.stdSimplex.δ_zero_toSSetObjIproof · cited by 1
- SSet.stdSimplex.δ_one_toSSetObjIproof · cited by 1
- TopCat.snd_iso_of_left_embedding_range_subsetproof · cited by 1
- AlgebraicGeometry.isomorphisms_eq_stalkwiseproof · cited by 0
- TopCat.isoOfHomeo_homstatement and proof · cited by 0
- TopCat.isoOfHomeo_invstatement and proof · cited by 0
- TopCat.nonempty_isColimit_iff_eq_coinducedproof · cited by 0
- TopCat.nonempty_isLimit_iff_eq_inducedproof · cited by 0
- TopCat.fst_iso_of_right_embedding_range_subsetproof · cited by 0
- TopCat.of_homeoOfIsostatement and proof · cited by 0