# Tag Info

### When did the Joyal model structure on simplicial sets originate?

My suspicion is now that it was some time between 2004 and 2006. I have a lot more citations in this blog post, but I note three points, in reverse chronological order: Multiple experts are referring ...
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### Complexity of coherence diagrams in an $n$-category

This is not a full answer to the question but it was too long for a comment. Depending on your conventions, "weak $n$-categories" might mean "$(n,n)$-categories" which are a ...
• 7,007
Accepted

### $\infty$-groupoid iff Kan condition

A good place to start is the following characterization of nerves of ordinary groupoids: A category is a groupoid if and only if its nerve is a Kan complex. Filling the outer horns is precisely what ...
• 30.3k