Questions tagged [internal-groupoids]

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Does the convolution $C^*$-algebra of locally compact Hausdorff groupoids recover back the respective groupoid?

First of all, my knowledge of operator algebras (and functional analysis) is very superficial, so sorry if the answer is actually well-known. Let $X$ be a locally compact Hausdorff groupoid (or Lie ...
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Explicit description of the canonical $\pi_G: \mathrm{Sh}(G_0)\to B_S(\mathbf{G})$

Given a localic groupoid $\mathbf{G} = (G_1\overset{d_0}{\underset{d_1}{\rightrightarrows}}G_0)$ and letting $B\mathbf{G}$ denote its classifying topos, I'm looking for a explicit description of the ...
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2 votes
1 answer
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What is the difference between Path $\infty$-groupoid and Smooth Fundamental $\infty$-groupoid of a smooth space?

A couple of days back I asked a question Is there a Geometric/Smooth version of Homotopy Hypothesis using the path $\infty$-Groupoid of a Smooth Space? in MO about the existence of a possible Smooth/...
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1 vote
1 answer
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Is there an operad that codifies groupoids?

maybe this question is trivial and, then this is the reason I've never seen this written. The motivation is to define internal $\infty$-groupoids (that are preferably) Kan fibrant and to see if Kan ...
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7 votes
2 answers
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Reference for a path groupoid being a diffeological groupoid

I am looking for a reference that has a proof that a path groupoid is a groupoid internal to the category of diffeological spaces. I do know how to prove this fact, and a proof is not hard. My reason ...
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2 votes
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Which makes Lie groupoids so nice?

This is a continuation of my previous question. A) Morphisms in (1') are basically internal anafunctors, their compositions heavily use (and only) pullback/limit. B) Bibundles in (2) are basically ...
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3 votes
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When is a category of groupoid schemes fibred over schemes?

The category of topological categories $Cat(Top)$ is fibred over $Top$ - the functor sending a groupoid $X_1 \rightrightarrows X_0$ to its object space $X_0$ is a Grothendieck fibration. Now one can ...
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8 votes
1 answer
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Who first came up with the idea of essential/Morita equivalence of internal groupoids/categories?

The idea that stacks can be identified with groupoids internal to the base site $S$ up to what is variously called essential/Morita equivalence is well known. The basic idea is that one takes the 2-...
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