Theorems · Definition · category theory
CategoryTheory.Grpd.piIsoPi
(J : Type u) → (f : J → CategoryTheory.Grpd) → CategoryTheory.Grpd.of ((j : J) → ↑(f j)) ≅ ∏ᶜ f
The product of a family of groupoids is isomorphic to the product object in the category of Groupoids
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.Discretestatement · cited by 2,447
- CategoryTheory.Bundled.αstatement · cited by 736
- CategoryTheory.Discrete.functorstatement and proof · cited by 633
- CategoryTheory.Limits.piObjstatement · cited by 237
- CategoryTheory.Groupoidstatement · cited by 182
- CategoryTheory.Limits.limit.isLimitproof · cited by 146
- CategoryTheory.Limits.IsLimit.conePointUniqueUpToIsoproof · cited by 57
- CategoryTheory.Grpdstatement and proof · cited by 30
- CategoryTheory.Grpd.ofstatement · cited by 9
- CategoryTheory.Grpd.piLimitFanIsLimitproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Grpd.piIsoPi_hom_πstatement · cited by 0