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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.
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
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