Talk:Higher category theory
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Definitions
[edit]I dont think this is quite right. I dont think that the construction of n-categories uses enrichment, that is how you make the higher analogs of bicategories and tricategories. n-categories are gotten by a process called categorification which is like internalization. or maybe i am confused... but i am pretty sure enrihment gives you something different than an n-category, i have been to seminars where such is stated. Sean, a student 02:48, 19 May 2008 (UTC)
- There are several definitions for a higher category, but the most basic definition of strict n-categories uses enrichment recursively. Weak n-categories cannot be defined in terms of enrichment, or using weak enrichment, in physics, n-categories are generally weak so other definitions are used. Internalization, i.e. using internal categories, allows to define a type of n-categories. Categorification is the process to "categorize" and used in various contexts. Cenarium (talk) 17:24, 19 June 2008 (UTC)
Links
[edit]I added the links to the books by Simpson and Lurie, which show much of the modern picture on (infinity,1)-categories.
I removed however, the links to a (predominantly military-content) entry Network Science and also to entry Polytely. Despite the very very very very very superficial similarity, the entries have nothing substantial to do with category theory, especially with the higher category theory. The links are almost a spam. Zoran.skoda (talk) 16:06, 1 September 2010 (UTC)
Question
[edit]Are there strict categories that are not higher categories? All the best: Rich Farmbrough, 12:34, 4 September 2018 (UTC).
Purposes and Origins
[edit]The article might benefit from a section that explains what kind of problems higher categories solve, that are not captured by ordinary category theory and how those open problems started some of the research in this direction.
For example a description of fully local topological field theories required a notation of the (infinity,n)-category of cobordisms
2A01:598:D008:5611:F3E1:C62:C74:672C (talk) 20:05, 20 October 2022 (UTC)
N-Fold Segal Spaces
[edit]As it turned out, one of the most manageable descriptions of (infinity,n)-categories are the n-fold Segal spaces. Maybe write a least a link to a description of them. 2A01:598:D008:5611:F3E1:C62:C74:672C (talk) 20:07, 20 October 2022 (UTC)