Theorems · Definition · category theory
CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → (X : CategoryTheory.SimplicialObject.Augmented C) → X.rightOp.leftOp ≅ XConverting an augmented simplicial object to an augmented cosimplicial object and back is isomorphic to the given object.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.Comma.leftproof · cited by 886
- CategoryTheory.SimplicialObject.Augmentedstatement and proof · cited by 113
- CategoryTheory.eqToIsoproof · cited by 97
- CategoryTheory.SimplicialObject.Augmented.rightOpstatement · cited by 15
- CategoryTheory.CosimplicialObject.Augmented.leftOpstatement · cited by 14
- CategoryTheory.Functor.rightOpLeftOpIsoproof · cited by 8
- CategoryTheory.Comma.isoMkproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.simplicialCosimplicialAugmentedEquivproof · cited by 2
- CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_left_appstatement and proof · cited by 0
- CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_rightstatement and proof · cited by 0
- CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_inv_left_appstatement and proof · cited by 0
- CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_inv_rightstatement and proof · cited by 0