2
$\begingroup$

I have a question about a definition used in nLab article on $n$-groupoids: https://ncatlab.org/nlab/show/n-groupoid

What does it mean that "every parallel pair of $j$-morphisms is equivalent for $j>n$? Surely, that's not a research question, but I nowhere found an answer. Does that mean that the corresponending equilizers on $j$-level are equivalences? (just a guess of mine)

$\endgroup$

1 Answer 1

5
$\begingroup$

It means that between every two $j$-cells with the same domain and codomain ($j > n$), there is a $(j + 1)$-cell between them (which is necessarily an equivalence by the first condition of the definition on that page) exhibiting them as equivalent.

(Meta note: math.stackexchange is best suited for non-research-level mathematics questions.)

$\endgroup$
2
  • $\begingroup$ Addition to the meta note: also the category theory zulip community might be a good place to ask. $\endgroup$
    – Aurelio
    Jul 16, 2020 at 12:18
  • $\begingroup$ Further to @varkor's answer, I would recommend playing around with a homotopy-oriented proof assistant, for example Globular: it is an excellent way to acquire a hands-on intuition of "being equivalent up to higher cells". You can find a tutorial video for Globular by Jamie Vicary. $\endgroup$
    – Aurelio
    Jul 16, 2020 at 19:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.