Skip to main content

# Questions tagged [topological-stacks]

The tag has no usage guidance.

20 questions
Filter by
Sorted by
Tagged with
0 votes
1 answer
25 views

### Simplicial manifolds which do not satisfy Kan condition locally?

Similar to Kan condition for simplicial sets, there are also Kan condition for simplicial manifolds, that is, we ask the horn projection $p^k_j: X_k \to Hom(\Lambda[k,j], X)$ to be a surjective ...
5 votes
0 answers
96 views

### Stackification of finite categories

Assume I have a base category $\mathscr S$ with finite limits and a geometric morphism $\gamma :\mathscr S\to Fin$ into the category of finite sets (for example because $\mathscr S$ is positive ...
• 4,250
2 votes
0 answers
81 views

### The stack classifying non-oriented triangles is equivalent to a quotient stack $[\widetilde{T}/S_3]$

I come across problems when I try to compute the stack classifying non-oriented triangles. My reference is the book Algebriac Stacks ( K. Behrend, B. Conrad, D. Edidin, B. Fantechi, W. Fulton, L. ...
0 votes
1 answer
35 views

1 vote
1 answer
39 views

### Minimal site that induces a stack from a psuedofunctor

I'm working with Vistoli's definition of stacks [1] Let $\Phi:C^{op}\to {Cat}$ be a psudeofunctor. Is there always a minimal Grothendieck topology on $C$ such that it induces a stack? If not, are ...
• 247
2 votes
0 answers
255 views

### Higher stacks and BG

I am wondering how one should think of the higher stacks $B^n(G)$? Here is what I mean: The stack $BG$ can be thought of as the quotient of a point by the group $G$ ($BG = */G$) in the proper ...
• 1,043
2 votes
1 answer
216 views

### basic reference for stacks

I'd like a reference for a very basic definition of stacks Kashiwara's paper almost does it except for example writing such as for every open set U in the cover there is a cat C(U) so U --> C(U) is a ...
• 427
4 votes
1 answer
183 views

### Proposition 4.1 in Vistoli's notes on descent

Proposition 4.1 of Vistoli's notes says $\mathsf{Top}^2$ is a stack over $\mathsf{Top}$. The proof starts by looking at the fibered product $\coprod_iU_i \times _U\coprod_iU_i$, however this object ...
• 49
1 vote
0 answers
50 views

### $\mathsf{Top}^2$ is a stack over $\mathsf{Top}$?

In section 4.1 of Vistoli's notes he starts by showing we may locally construct arrows in $\mathsf{Top}^2$, i.e arrows over $U$. Then, the author says that we can moreover do the same for spaces, ...
• 11
7 votes
2 answers
417 views

### Relation between two notions of $BG$

The following is something that's always niggled me a little bit. I usually think about stacks over schemes, so I'm a bit out of my element—I apologize if I say anything silly below. Let $G$ be a ...
• 54.4k
1 vote
1 answer
225 views

### Differentiable stacks and morita morphism

I heard that if $[X_0/G_0]$ and $[X_1/G_1]$ are differentiable stacks, then any morphism between them is naturally equivalent to (G_0 \rightrightarrows X_0) \xleftarrow{\simeq} (G_2 \...
• 1,370
2 votes
1 answer
3k views

### How many sequences possible in stack , if the input(1,2,3,...,n) is in order?

How many permutations can be obtained in the output (in the same order) using a stack assuming that the input is the sequence $(1, 2, 3, 4, 5,\dots, n)$ in that order? Example If $n=5$, then outputs ...
• 4,797
2 votes
1 answer
474 views

### Is there a more general obstruction to the existence of moduli spaces than the existence of automorphisms?

We are taught that, in general: A type of objects that has nontrivial automorphisms cannot have a fine moduli space. The proof generally goes along the lines of: Take an object $X$ with a non-...
• 25.1k