# 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.

**8**

**1**answer

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

**2**

**1**answer

### Is it possible to characterize the elements of the C$^*$-algebra of an open subgroupoid?

**4**

**0**answers

### Restricting a function defined on an étale groupoid to an isotropy group

**4**

**1**answer

### Hopf “algebroid” structure of a groupoid convolution algebra?

**6**

**1**answer

### Amenable groupoid C*-algebras satisfy the UCT in English?

**11**

**3**answers

### Elementary theory of the category of groupoids?

**2**

**0**answers

### Classifying space induces a equivalence of categories between $\operatorname{PBun}_G(M)$ and $\Pi(M,BG)$ for finite groups $G$

**2**

**0**answers

### A quantity associated to a foliated manifold and its non-commutative interpretation

**1**

**0**answers

### Classification of all groupoids $G$ whose automorphism group is in bijective correspondence the automorphism group of $C^*_\text{red}(G)$

**3**

**0**answers

### Skeleton of $\mathcal{G}$-simplicial complex

**4**

**1**answer

### Delooping of a group object as a one object groupoid

**3**

**0**answers

### Non-commutative duality II: The two algebras of a groupoid

**14**

**3**answers

### Non-commutative duality I: Which C*-algebras are (isomorphic to a) convolution algebra?

**7**

**0**answers

### Is there a practically useful or concrete representation theory/Fourier analysis on finite groupoids?

**3**

**1**answer

### Morphisms of $\infty$-groupoids

**6**

**1**answer

### Representation of fundamental groupoid as $2$-sheaf

**5**

**0**answers

### Representations of 2-groups and quantum double constructions

**6**

**0**answers

### Is there a Geometric/Smooth version of Homotopy Hypothesis using the path $\infty$-Groupoid of a Smooth Space?

**1**

**0**answers

### Promoting representation of a subgroup to representation of an action groupoid

**18**

**1**answer

### What is the groupoid cardinality of the category of vector spaces over a finite field?

**8**

**0**answers

### What are the Newton groupoids from Drinfeld's paper on the Grinberg-Kazhdan theorem?

**6**

**1**answer

### Integrating the Riemann curvature tensor over a singular 2-disc

**1**

**0**answers

### 1-connected infinity groupoids, groupoids and 1-connected spaces

**4**

**1**answer

### Homotopy of functors

**1**

**1**answer

### Property of representations of reductive group schemes over characteristic 0 field

**6**

**0**answers

### J. F. Adams Proof of Cellular Approximation Theorem

**6**

**3**answers

### Which $\infty$-groupoids correspond to simplicial abelian groups?

**4**

**0**answers

### Inverse semigroups and partial symmetries

**11**

**1**answer

### Space with semi-locally simply connected open subsets

**5**

**1**answer

### Homologous quotient of fundamental groupoid

**-4**

**1**answer

### Does the 1-category construction of a topos of presheaves extend to the 2-Category of Groupoids?

**6**

**1**answer

### Is the 2-сategory of groupoids locally presentable?

**5**

**3**answers

### Generalize $H^1_{dR}(X)=\mathrm{Hom} (\pi_1(X),\mathbb R)$ to fundamental Groupoid

**7**

**4**answers

### On fundamental groupoid of fundamental groupoid

**2**

**0**answers

### Equivalence De Rham and Dolbeault groupoids

**3**

**0**answers

### Restricting functions to an isotropy group

**3**

**0**answers

### What category of toposes is monadic over the 2-category of groupoids?

**5**

**1**answer

### Automorphism group of a torsor

**4**

**0**answers

### What is the category of algebras for the finitely supported measures monad?

**3**

**1**answer

### Continuity of functions on étale groupoids

**3**

**0**answers

### Cencov's “categories of figures”

**2**

**1**answer

### Convolution product in an étale groupoid

**2**

**0**answers

### Fundamental groupoid and fibration

**60**

**4**answers

### Why did Voevodsky consider categories “posets in the next dimension”, and groupoids the correct generalisation of sets?

**1**

**0**answers

### Does the 2 category of Groupoids Admit the Vector Space Monad?

**3**

**1**answer

### Is Quillen's bracket a “universal enveloping” something?

**3**

**1**answer

### Slice theorem for proper groupoids

**8**

**0**answers

### Frobenius monads and groupoids

**10**

**1**answer

### The étale topos of a scheme is the classifying topos of which groupoid?

**0**

**2**answers