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Results tagged with groupoids
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user 11640
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.
3
votes
Accepted
Groupoid as a 2-coequaliser
Your claim is incorrect because you truncated the simplicial diagram too much. Indeed, if what you said were true, then the isomorphism class of a group would be determined by its cardinality, but thi …
- 15.9k
10
votes
Accepted
Toposes (topoi) as classifying toposes of groupoids
Perhaps these slides will be helpful. I'll try to explain what happens in your special case.
Let $M$ be a monoid and let $\mathcal{B} M$ be the topos of right $M$-sets. The points of $\mathcal{B} M$ …
- 15.9k
5
votes
Does the nerve functor (resp. fundamental groupoid functor) preserve homotopy colimits (resp...
The nerve functor does not preserve homotopy colimits. Indeed, take any simplicial set $X$ with non-trivial $\pi_n$ ($n > 1$) and consider $X$ as a simplicial diagram of sets. In $\mathbf{sSet}$, its …
- 15.9k