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Theorems · Definition · algebraic topology

FundamentalGroupoidFunctor.piTopToPiCone

{I : Type u} →
  (X : I → TopCat) →
    CategoryTheory.Limits.Fan.mk (FundamentalGroupoid.fundamentalGroupoidFunctor.obj (TopCat.of ((i : I) → ↑(X i))))
        (FundamentalGroupoidFunctor.proj X) ⟶
      CategoryTheory.Grpd.piLimitFan fun i => FundamentalGroupoid.fundamentalGroupoidFunctor.obj (X i)

This is piIso.inv as a cone morphism (in fact, isomorphism)

Defined in
Mathlib.AlgebraicTopology.FundamentalGroupoid.Product
Cited by
1 results in Mathlib
Foundations
Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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FundamentalGroupoidFunctor.preservesProduct · cited by 0FundamentalGroupoidFuncto…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objTopCat.carrier · cited by 3184TopCat.carrierCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteTopCat · cited by 1889TopCatCategoryTheory.Discrete.functor · cited by 633Discrete.functorCategoryTheory.Limits.Fan · cited by 52Limits.FanCategoryTheory.Limits.Fan.mk · cited by 46Fan.mkCategoryTheory.Grpd · cited by 30CategoryTheory.GrpdCategoryTheory.Functor.pi' · cited by 23Functor.pi'FundamentalGroupoid.fundamentalGroupoidFunctor · cited by 21FundamentalGroupoid.funda…FundamentalGroupoidFunctor.proj · cited by 3FundamentalGroupoidFuncto…CategoryTheory.Grpd.piLimitFan · cited by 1Grpd.piLimitFanFundamentalGroupoidFunctor.pi…CITED BYCITES

Cites13

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