# Tagged Questions

0answers
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### Torsors for 2-groups

Let $\mathbb{G}$ be a 2-group, by which I mean a strict monoidal category in which all objects are invertible (up to coherent isomorphisms) and all morphisms are invertible (strictly). What is the ...
1answer
216 views

### Where to get help with Homotopy type theory?

I'm trying to understand the Homotopy Type Theory book. I find myself completely lost in Chapter 2, especially when it starts using higher groupoids. What is the recommended background for this book? ...
1answer
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### Should the first be the last by composition of paths?

Given two paths $f,g:\mathbb{I}\rightarrow X$ with $f\left(1\right)=g\left(0\right)$ there is a composite $f.g$ defined by $t\mapsto f\left(2t\right)$ if $2t\leq1$ and $t\mapsto g\left(2t-1\right)$ ...
3answers
375 views

### Statement about Homotopy in Brown's “Topology & Groupoids”

I am trying to understand a statement in Brown's Topology and Groupoids, 7.2.5 (Corollary 1), page 270. Let's first have some preliminary remarks Let $X,Y$ be topological spaces. The track groupoid ...
3answers
244 views

### can the statement “a simplicial set is the nerve of a category if and only if it satisfies a horn-filling condition” be tweaked for groupoids?

For some reason I convinced myself that a simplicial set (or maybe I mean directly Kan complex) is homotopy equivalent to the nerve of a groupoid if and only if it has no higher homotopy groups. Is ...
1answer
236 views

### Topological Space as an $(\infty,0)$-category

Given a topological space $X$, we may wish to consider it as an $(\infty,0)$-category, where the objects are the points of the space, the 1-morphisms are continuous paths between points, the ...
4answers
349 views

### What are the ramifications of the fact that the first homotopy group can be non-commutative, whilst the higher homotopy groups can't be?

Does this mean that the first homotopy group in some sense contains more information than the higher homotopy groups? Is there another generalization of the fundamental group that can give rise to ...