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Theorems · Definition · category theory

CategoryTheory.SimplicialObject.Augmented

(C : Type u) → [CategoryTheory.Category.{v, u} C] → Type (max u v)

The category of augmented simplicial objects, defined as a comma category.

Defined in
Mathlib.AlgebraicTopology.SimplicialObject.Basic
Cited by
113 results in Mathlib
Foundations
Depth 32 from the axioms, rests on 300 definitions · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy · cited by 24Augmented.ExtraDegeneracyAugmentedSimplexCategory.equivAugmentedSimplicialObject · cited by 23AugmentedSimplexCategory.…CategoryTheory.Arrow.augmentedCechNerve · cited by 16Arrow.augmentedCechNerveCategoryTheory.SimplicialObject.Augmented.rightOp · cited by 15Augmented.rightOpCategoryTheory.SimplicialObject.Augmented.toArrow · cited by 15Augmented.toArrowCategoryTheory.CosimplicialObject.Augmented.leftOp · cited by 14Augmented.leftOpCategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s · cited by 13ExtraDegeneracy.sCategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s' · cited by 11ExtraDegeneracy.s'CategoryTheory.SimplicialObject.Augmented.drop · cited by 10Augmented.dropCategoryTheory.SimplicialObject.Augmented.point · cited by 10Augmented.pointCategoryTheory.SimplicialObject.augmentedCechNerve · cited by 7SimplicialObject.augmente…CategoryTheory.SimplicialObject.Augmented.const · cited by 7Augmented.constCategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.section_ · cited by 7ExtraDegeneracy.section_CategoryTheory.SimplicialObject.augmentOfIsTerminal · cited by 6SimplicialObject.augmentO…SSet.Augmented · cited by 5SSet.AugmentedCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.id · cited by 3333Functor.idCategoryTheory.Comma · cited by 566CategoryTheory.CommaCategoryTheory.SimplicialObject · cited by 548CategoryTheory.Simplicial…CategoryTheory.SimplicialObject.const · cited by 110SimplicialObject.constSimplicialObject.AugmentedCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by161

Results whose statement or proof uses this declaration.