Timeline for Are dagger-categories / categories with duality related to unoriented field theories?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 5 at 20:33 | vote | accept | Tim Campion | ||
| Nov 5 at 14:28 | answer | added | Luuk Stehouwer | timeline score: 1 | |
| Nov 9, 2023 at 8:06 | comment | added | Urs Schreiber | There is apparently a 12-author article coming up with more discussion, talk notes here: ncatlab.org/nlab/show/dagger+category#ReferencesHigherDagger | |
| Apr 12, 2023 at 15:00 | comment | added | Simon Henry | [...] of an $\infty$-groupoid $X$ and an object $C$ of $Cat_\infty^{C_2}$ together with a morphism $X \to C$ in $Cat_\infty^{C_2}$ which when seen as a morphism in $Cat_\infty$ is a (non-full) subcategory inclusion which is subjective on objects. And then we impose a Segal type condition that forces $X$ to be the groupoid of dagger-isomorphisms in $C$. | |
| Apr 12, 2023 at 15:00 | comment | added | Simon Henry | The problem with the definition you propose is that it miss the key condition "acts trivially on objects". I think the correct definition can be expressed as follows: the action of $C_2$ on $Cat_\infty$ by taking the opposite category restrict to a "trivial" action on the full subcategory $Gpd_\infty \subset Cat_\infty$. That is we have a functor $Gpd_\infty \to Cat_\infty^{C_2}$. An $\infty$-dagger category is a pair [...] | |
| Apr 12, 2023 at 14:53 | comment | added | Simon Henry | The correct $\infty$-categorical generalization of dagger categories is a little more complicated than this - you need to include the groupoids of objects and "dagger-isomorphism" between them as part of the structure. This was considered here mathoverflow.net/questions/220032/… (see Peter Lumsdain answer) | |
| Apr 12, 2023 at 14:49 | history | asked | Tim Campion | CC BY-SA 4.0 |