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Theorems · Definition · category theory

CategoryTheory.SimplicialObject.const

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

The constant simplicial object is the constant functor.

Defined in
Mathlib.AlgebraicTopology.SimplicialObject.Basic
Cited by
110 results in Mathlib
Foundations
Depth 31 from the axioms, rests on 297 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 · cited by 113SimplicialObject.AugmentedCategoryTheory.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.Augmented.const · cited by 7Augmented.constCategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.section_ · cited by 7ExtraDegeneracy.section_CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.homotopy.h · cited by 3homotopy.hCategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.s'_comp_ε · cited by 2ExtraDegeneracy.s'_comp_εCategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.section_app_comp_hom_app · cited by 2ExtraDegeneracy.section_a…CategoryTheory.SimplicialObject.Augmented.ExtraDegeneracy.homotopy · cited by 1ExtraDegeneracy.homotopyCategoryTheory.SimplicialObject.augment_hom_app · cited by 1SimplicialObject.augment_…AlgebraicTopology.AlternatingFaceMapComplex.ε_app_f_zero · cited by 1AlternatingFaceMapComplex…CategoryTheory.SimplicialObject.Augmented.hom_ext · cited by 1Augmented.hom_extCategoryTheory.SimplicialObject.Augmented.w_app · cited by 1Augmented.w_appCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorOpposite · cited by 8081OppositeSimplexCategory · cited by 2204SimplexCategoryCategoryTheory.Functor.const · cited by 1264Functor.constCategoryTheory.SimplicialObject · cited by 548CategoryTheory.Simplicial…SimplicialObject.constCITED BYCITES

Cites6

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Cited by123

Results whose statement or proof uses this declaration.