mathlib documentation

category_theory.category.Groupoid

Category of groupoids #

This file contains the definition of the category Groupoid of all groupoids. In this category objects are groupoids and morphisms are functors between these groupoids.

We also provide two “forgetting” functors: objects : Groupoid ⥤ Type and forget_to_Cat : Groupoid ⥤ Cat.

Implementation notes #

Though Groupoid is not a concrete category, we use bundled to define its carrier type.

@[nolint]
def category_theory.Groupoid  :
Type (max (u+1) u (v+1))

Category of groupoids

Equations

Construct a bundled Groupoid from the underlying type and the typeclass.

Equations
@[instance]

Category structure on Groupoid

Equations

Functor that gets the set of objects of a groupoid. It is not called forget, because it is not a faithful functor.

Equations

Forgetting functor to Cat

Equations