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Theorems · Definition · algebraic topology

FundamentalGroupoidFunctor.coneDiscreteComp

{I : Type u} →
  (X : I → TopCat) →
    CategoryTheory.Limits.Cone
        ((CategoryTheory.Discrete.functor X).comp FundamentalGroupoid.fundamentalGroupoidFunctor) ≌
      CategoryTheory.Limits.Cone
        (CategoryTheory.Discrete.functor fun i => FundamentalGroupoid.fundamentalGroupoidFunctor.obj (X i))

Equivalence between the categories of cones over the objects π Xᵢ written in two ways

Defined in
Mathlib.AlgebraicTopology.FundamentalGroupoid.Product
Cited by
2 results in Mathlib
Foundations
Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
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FundamentalGroupoidFunctor.coneDiscreteComp_obj_mapCone · cited by 0FundamentalGroupoidFuncto…FundamentalGroupoidFunctor.preservesProduct · cited by 0FundamentalGroupoidFuncto…CategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteTopCat · cited by 1889TopCatCategoryTheory.Limits.Cone · cited by 710Limits.ConeCategoryTheory.Discrete.functor · cited by 633Discrete.functorCategoryTheory.Equivalence · cited by 601CategoryTheory.EquivalenceCategoryTheory.Grpd · cited by 30CategoryTheory.GrpdFundamentalGroupoid.fundamentalGroupoidFunctor · cited by 21FundamentalGroupoid.funda…CategoryTheory.Limits.Cone.postcomposeEquivalence · cited by 12Cone.postcomposeEquivalen…CategoryTheory.Discrete.compNatIsoDiscrete · cited by 11Discrete.compNatIsoDiscre…FundamentalGroupoidFunctor.co…CITED BYCITES

Cites11

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