# Questions tagged [internal-groupoids]

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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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### 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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### 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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### 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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### 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-...