Theorems · Definition · category theory
FintypeCat.uSwitchEquiv
(X : FintypeCat) → (FintypeCat.uSwitch.obj X).obj ≃ X.obj
Switching the universe of an object X : FintypeCat.{u} does not change X up to equivalence
of types. This is natural in the sense that it commutes with uSwitch.map f for
any f : X ⟶ Y in FintypeCat.{u}.
- Defined in
- Mathlib.CategoryTheory.FintypeCat
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement · cited by 19,642
- Equivstatement · cited by 8,337
- Equiv.symmproof · cited by 3,681
- Finitestatement · cited by 3,029
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement and proof · cited by 1,316
- Equiv.transproof · cited by 337
- FintypeCatstatement and proof · cited by 217
- Equiv.uliftproof · cited by 115
- Fintype.equivFinproof · cited by 51
- FintypeCat.uSwitchstatement · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- FintypeCat.uSwitchEquiv_naturalitystatement · cited by 1
- FintypeCat.uSwitchEquiv_symm_naturalitystatement and proof · cited by 0
- FintypeCat.uSwitchEquivalenceproof · cited by 0
- FintypeCat.uSwitch_map_uSwitch_mapstatement · cited by 0