# Questions tagged [groupoids]

A groupoid is a category where all morphisms are invertible. This notion can also be seen as an extension of the notion of group. A motivating example is the fundamental groupoid of a topological space with respect to several base points, compared to the usual fundamental group.

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### Filtered 2-colimits commute with finite 2-limits

Is there an explicit proof anywhere in the literature that filtered 2-colimits commute with finite 2-limits (all meant in the weak bicategorical sense) in the 2-category of groupoids? I have only ...
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### Representations of 2-groups and quantum double constructions

Let $G$ be a finite group. The category of its representations (complex linear, finite dimensional, throughout this whole question) is equivalent to $\mathbb{C}[G]$-modules. V. Drinfeld constructed a ...
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### Is there a Geometric/Smooth version of Homotopy Hypothesis using the path $\infty$-Groupoid of a Smooth Space?

A version of Homotopy Hypothesis says that the Fundamental $n$-grupoids model Homotopy $n$-types... and if we continue upto $\infty$, then the Fundamental $\infty$- groupoids or Kan Complexes model ...
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### Promoting representation of a subgroup to representation of an action groupoid

Suppose I have a group $G$, a subgroup $K \leq G$, and a representation $(\sigma, V)$ of $K$. There is a natural left action of $G$ on $X := G/K \times G/K$ given by $g \cdot (g'K,g''K) = (gg'K,gg''K)$...
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### Homologous quotient of fundamental groupoid

Let $X$ be a connected space and $\Pi_1(X)$ be its fundamental groupoid. We consider the homologous relation $\mathcal R$ on every morphism space: $f,g\in \Pi_1(X)(p,q)$ are related if the singular ...
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### Does the 1-category construction of a topos of presheaves extend to the 2-Category of Groupoids?

In the case of 1-categories, we know there is a functor category $PSh(C):=[C^{op},Set]$, where $C$ is a small category, and this functor category is a topos. I am hoping this will extend to the case ...