Theorems · Definition · category theory

CategoryTheory.CosimplicialObject.Augmented.leftOp

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    CategoryTheory.CosimplicialObject.Augmented Cᵒᵖ → CategoryTheory.SimplicialObject.Augmented C

Construct an augmented simplicial object from an augmented cosimplicial object in the opposite category.

Defined in: Mathlib.AlgebraicTopology.SimplicialObject.Basic
Cited by: 14 results in Mathlib
Foundations: Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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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.Categorystatement and proof · cited by 32,673
Oppositestatement and proof · cited by 8,081
Opposite.unopproof · cited by 2,231
CategoryTheory.Comma.leftproof · cited by 886
CategoryTheory.Comma.rightproof · cited by 727
CategoryTheory.Comma.homproof · cited by 490
CategoryTheory.Functor.leftOpproof · cited by 187
CategoryTheory.SimplicialObject.Augmentedstatement · cited by 113
CategoryTheory.CosimplicialObject.Augmentedstatement and proof · cited by 72
CategoryTheory.NatTrans.leftOpproof · cited by 17

Cited by17

Results whose statement or proof uses this declaration.

CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIsostatement · cited by 4
CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIsostatement · cited by 4
CategoryTheory.cosimplicialToSimplicialAugmentedproof · cited by 3
CategoryTheory.CosimplicialObject.Augmented.leftOpRightOpIso_inv_right_appstatement · cited by 0
CategoryTheory.CosimplicialObject.Augmented.leftOp_hom_appstatement and proof · cited by 0
CategoryTheory.CosimplicialObject.Augmented.leftOp_left_mapstatement and proof · cited by 0
CategoryTheory.CosimplicialObject.Augmented.leftOp_left_objstatement and proof · cited by 0
CategoryTheory.CosimplicialObject.Augmented.leftOp_rightstatement and proof · cited by 0
CategoryTheory.cosimplicialToSimplicialAugmented_mapstatement · cited by 0
CategoryTheory.cosimplicialToSimplicialAugmented_objstatement · cited by 0
CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_left_appstatement · cited by 0
CategoryTheory.SimplicialObject.Augmented.rightOpLeftOpIso_hom_rightstatement · cited by 0