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Results tagged with groupoids
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user 22131
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.
9
votes
A possible alternative model for $\infty$-groupoids
surprised if the fibrant objects of that model structure would be related to the sort of condition you are talking about - but in any case these fibrants objects produces an acceptable notion of $\infty$-groupoids …
- 42.4k
22
votes
Accepted
Is there a higher analog of "category with all same side inverses is a groupoid"?
Yes, this is possible. The following is a classical result of the theory of quasi-categories (You'll find it in the early part of Lurie's Higher topos theory or in Joyal notes on quasi-categories - w …
- 63.1k
18
votes
Accepted
Non-commutative duality I: Which C*-algebras are (isomorphic to a) convolution algebra?
without having a clear geometric origin (well, I'm sure one can find a geometric explanation for Fourier duality, but what I mean is that it cannot be interpreted as a morphisms or bibundle between the groupoids …
- 42.4k
73
votes
Accepted
Why did Voevodsky consider categories "posets in the next dimension", and groupoids the corr...
It is in this sense that groupoids are "higher dimensional sets" and categories are groupoids with a structure. … (The $(\infty,1)$-categorical Yoneda lemma is in terms of functors to the category of $\infty$-groupoids etc...) …
- 28.1k
1
vote
Accepted
Certain groupoid and its $C^{*}$ algebra
For each other generator tat we need to freely add one can add instead an automorphism of the object $1$ in order to get an equivalent groupoids. … Hence your groupoids is equivalent to the groups with one generator for each pair $i<j$ of $\{1 \dots,n\}$ whcih are at distance at least $2$ and there is exactly $k=(n-2)(n-3)/2$ such pairs. …
- 42.4k
2
votes
0
answers
119
views
Are all locally compact anisotropic groupoids etale up to equivalence?
They are the same as r-discrete groupoids.
All the examples of anisotropic locally compact groupoids I know also happen to be equivalent to etale groupoids. … There is a similar construction for Lie groupoids whose isotropy groups are discrete. …
- 42.4k