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Theorems · Definition · category theory

CategoryTheory.Limits.sigmaConst

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

The functor sending (X, n) to the coproduct of copies of X indexed by n.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.Products
Cited by
18 results in Mathlib
Foundations
Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasCoproducts
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Around this declaration

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

SSet.normalizedChainComplex · cited by 29SSet.normalizedChainCompl…SSet.toNormalizedChainComplex · cited by 20SSet.toNormalizedChainCom…SSet.fromNormalizedChainComplex · cited by 12SSet.fromNormalizedChainC…SSet.π₀.fromChainComplexXZero · cited by 7π₀.fromChainComplexXZeroSheafOfModules.freeFunctor · cited by 4SheafOfModules.freeFunctorSSet.chainComplexFunctor · cited by 3SSet.chainComplexFunctorSSet.fromNormalizedChainComplex_toNormalizedChainComplex · cited by 2SSet.fromNormalizedChainC…SSet.homotopyEquivNormalizedChainComplex · cited by 2SSet.homotopyEquivNormali…SSet.PInfty_toNormalizedChainComplex · cited by 2SSet.PInfty_toNormalizedC…SSet.toNormalizedChainComplex_f_fromNormalizedChainComplex_f · cited by 2SSet.toNormalizedChainCom…SSet.toNormalizedChainComplex_fromNormalizedChainComplex · cited by 2SSet.toNormalizedChainCom…TopCat.singularHomology₀Iso · cited by 2TopCat.singularHomology₀I…SSet.ιNormalizedChainComplex_fromNormalizedChainComplex_f · cited by 2SSet.ιNormalizedChainComp…SSet.isColimitCokernelCoforkChainComplexDOneZero · cited by 1SSet.isColimitCokernelCof…AlgebraicTopology.singularChainComplexFunctorIsoOfTotallyDisconnectedSpace · cited by 1AlgebraicTopology.singula…DFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homCategoryTheory.Limits.sigmaObj · cited by 302Limits.sigmaObjCategoryTheory.Limits.HasCoproducts · cited by 119Limits.HasCoproductsCategoryTheory.Limits.Sigma.map' · cited by 24Sigma.map'CategoryTheory.Limits.Sigma.map · cited by 14Sigma.mapLimits.sigmaConstCITED BYCITES

Cites10

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

Cited by30

Results whose statement or proof uses this declaration.