Timeline for n-categorical pasting diagram overview
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 19, 2018 at 8:56 | comment | added | Harry Gindi | @Simon I was waiting for Amar to make that paper public since Marseilles. Now i've gotta check it out! | |
| Oct 19, 2018 at 8:51 | comment | added | Simon Henry | For the record, while Steiner's 1993 construction is indeed less convenient for computation it is also vastly more general than all the other due to the fact that it allows the diagram to only be well behaved on some "partial sub-categories". For example in arxiv.org/pdf/1806.10353.pdf, Amar Hadzihasanovic has shown that all "regular polygraphs" fits into Steiner directed complex machinery, this is considerably more than what you can do with any of the other notions. But I definitely that the ADC point of view is extremely powerful for computation. | |
| Aug 11, 2017 at 18:01 | comment | added | Harry Gindi | Also, not having read Simon's paper, I'm not sure if his generalized theory of pasting diagrams can be interpreted using chain complexes by modifying the definition of a loop-free basis. I'm also not convinced that it's really necessary in practice to consider a more general definition. All of the ordinary (and extraordinary) pasting diagrams I've run into can be formulated with ADCs (including the monster coherence diagrams in e.g. Todd Trimble's defn of tetracategories). Whiskered cells are just cells with their src&target summed with basis elements lower in the complex, etc. | |
| Aug 11, 2017 at 0:05 | comment | added | Harry Gindi | To avoid bumping again, just mentioning that to find the source and target of a cell in the ADC, you apply the boundary map of the chain complex, and the sum of the 'negative' elements becomes the source while the sum of the 'positive' elements becomes the target, roughly speaking. | |
| Aug 10, 2017 at 23:52 | history | edited | Harry Gindi | CC BY-SA 3.0 |
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| Aug 10, 2017 at 22:01 | history | edited | Harry Gindi | CC BY-SA 3.0 |
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| Aug 10, 2017 at 21:54 | history | answered | Harry Gindi | CC BY-SA 3.0 |