Timeline for The advantage of asymmetric objects
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 30, 2022 at 18:07 | comment | added | Peter LeFanu Lumsdaine | [cont’d] …and (2) the Théoreme de rigidité (Cor 2.6.2), which seems to maybe kinda-sorta link the two senses — its main hypothesis is polarisability, closely related to existence of duals, and its conclusion is a uniqueness-up-to-unique-equivalence result? So it looks like the “duals” sense is quite possibly based on the older “no non-trivial automorphisms” sense, because they’re somehow connected in the specific setting of Tannakian categories. But the precise connection is still not clear to me, without reading the book or knowing the topic properly! | |
| Jun 30, 2022 at 18:07 | comment | added | Peter LeFanu Lumsdaine | @SamHopkins: OK, looking it into a little, the earliest use of “rigid” for “all objects dualisable” I can find is in Saavedra Rivano 1972 Catégories Tanakiennes, LNM 265 (the book, not the short paper of the same title+date) — at least, he doesn’t cite any earlier source for the term/definition. He doesn’t explain the term when he introduces it, and I haven’t read the book fully, but on a quick skim, there are a couple of possible hints towards the motivation: (1) he earlier uses “rigid groupoid” to mean “essentially discrete groupoid” (i.e. all automorphisms are identities); and… [cont’d] | |
| Jun 30, 2022 at 17:49 | comment | added | Peter LeFanu Lumsdaine | @SamHopkins: I’ve wondered the same, and feel equally embarrassed to have no answer… | |
| Jun 30, 2022 at 17:34 | comment | added | Sam Hopkins | This is completely an aside, but one thing I'm embarrassed to never have properly understood is whether there is some deeper connection between this use of "rigid" and another common use of "rigid" in category theory to mean "objects have duals" (e.g. rigid monoidal category). Is that just a coincidence of terminology? | |
| Jun 30, 2022 at 17:23 | history | answered | Peter LeFanu Lumsdaine | CC BY-SA 4.0 |