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Questions tagged [internal-groupoids]

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1
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1answer
229 views

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 ...
6
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2answers
256 views

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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0answers
230 views

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 ...
3
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0answers
220 views

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 ...
5
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1answer
470 views

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-...