Theorems · Definition · category theory
CategoryTheory.Groupoid.isoEquivHom
{C : Type u} → [inst : CategoryTheory.Groupoid C] → (X Y : C) → (X ≅ Y) ≃ (X ⟶ Y)In a groupoid, isomorphisms are equivalent to morphisms.
- Defined in
- Mathlib.CategoryTheory.Groupoid
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Groupoid
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.Homstatement and proof · cited by 32,603
- Equivstatement · cited by 8,337
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.Groupoidstatement and proof · cited by 182
- CategoryTheory.Groupoid.invproof · cited by 36
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.Iso.coreproof · cited by 11
- CategoryTheory.Core.isoMkproof · cited by 2
- CategoryTheory.Groupoid.isIsomorphic_iff_nonempty_homproof · cited by 0
- CategoryTheory.Groupoid.isoEquivHom_applystatement and proof · cited by 0
- CategoryTheory.Groupoid.isoEquivHom_symm_apply_homstatement and proof · cited by 0
- CategoryTheory.Groupoid.isoEquivHom_symm_apply_invstatement · cited by 0
- FundamentalGroup.fundamentalGroupMulEquivOfPathproof · cited by 0