Fundamental groupoid of punit #
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The fundamental groupoid of punit is naturally isomorphic to category_theory.discrete punit
@[protected, instance]
def
fundamental_groupoid.quiver.hom.subsingleton
{x y : fundamental_groupoid punit} :
subsingleton (x ⟶ y)
Equivalence of groupoids between fundamental groupoid of punit and punit
Equations
- fundamental_groupoid.punit_equiv_discrete_punit = category_theory.equivalence.mk (category_theory.functor.star (fundamental_groupoid punit)) ((category_theory.functor.const (category_theory.discrete punit)).obj punit.star) (category_theory.nat_iso.of_components (λ (_x : fundamental_groupoid punit), category_theory.eq_to_iso _) fundamental_groupoid.punit_equiv_discrete_punit._proof_2) (((category_theory.functor.const (category_theory.discrete punit)).obj punit.star ⋙ category_theory.functor.star (fundamental_groupoid punit)).punit_ext (𝟭 (category_theory.discrete punit)))