Timeline for Existence of an addition bifunctor for the category of groups
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 30, 2020 at 8:18 | history | edited | Sebastien Palcoux | CC BY-SA 4.0 |
added 154 characters in body
|
| Jan 30, 2020 at 8:13 | vote | accept | Sebastien Palcoux | ||
| Jan 30, 2020 at 8:13 | history | edited | Sebastien Palcoux | CC BY-SA 4.0 |
cut the part about a multiplication bifunctor to be pasted as a dedicated post
|
| Jan 30, 2020 at 3:30 | answer | added | Martin Brandenburg | timeline score: 6 | |
| Jan 30, 2020 at 2:17 | history | edited | Sebastien Palcoux | CC BY-SA 4.0 |
reformulation in term of bifunctor
|
| Jan 29, 2020 at 16:13 | comment | added | Martin Brandenburg | Ok, I understand. A monoidal structure is even stronger than your initial requirement, but also more interesting. Now you got me ... ^^ | |
| Jan 29, 2020 at 12:40 | review | Close votes | |||
| Feb 3, 2020 at 3:05 | |||||
| Jan 29, 2020 at 12:06 | comment | added | Sebastien Palcoux | @MartinBrandenburg: We could ask whether the category $\mathcal{Grp}$ (or the subcategory of countable groups) admits a monoidal structure with unit $I \simeq C_0$ and $C_n \otimes C_m \simeq C_{n+m}$ (or with unit $I \simeq C_1$ and $C_n \otimes C_m \simeq C_{nm}$). | |
| Jan 29, 2020 at 11:49 | comment | added | Sebastien Palcoux | It was not really true to say << my motivation here is not in category theory >> because my motivation is in fact an eventual extension to subfactor theory, which is stronlgy related to tensor/fusion category theory. | |
| Jan 29, 2020 at 10:26 | comment | added | Sebastien Palcoux | @MartinBrandenburg I am in a dilemma: On one hand I don't see an easy/natural way to define such an addition (or multiplication) functor, but it can still exist. On the other hand, removing the category structure would allow arbitrary answers, which is not interesting. Something more subtle is required, and the category theory could help. | |
| Jan 29, 2020 at 10:07 | comment | added | Martin Brandenburg | @SebastienPalcoux When your motivation is not category theory, I suggest to rephrase the question accordingly and also remove the ct-tag. | |
| Jan 29, 2020 at 9:38 | history | edited | Sebastien Palcoux | CC BY-SA 4.0 |
replace "the addition functor" by "an addition functor". In fact it is not clear that such a functor exist...
|
| Jan 29, 2020 at 9:24 | comment | added | user44191 | I'm...strongly doubtful that there's a natural "addition" functor, and weakly doubtful that there's a natural "multiplication" functor. But if you do go with "set" and "map", then from what I can see, there's no interesting "structure" to $\tilde{A}$ - the extension can be defined completely arbitrarily. | |
| Jan 29, 2020 at 8:56 | comment | added | Sebastien Palcoux | @user44191 I should replace "category" by "set" and "functor" by "map" because my motivation here is not in category theory and I don't see a natural way to define these addition and multiplication functors; do you? | |
| Jan 29, 2020 at 8:15 | comment | added | Sebastien Palcoux | @user44191 Your comment is relevant! | |
| Jan 29, 2020 at 5:53 | comment | added | user44191 | How are you defining your category of cyclic groups (what are its morphisms), and how are you defining your addition and multiplication functors (what does each do to those morphisms)? | |
| Jan 29, 2020 at 5:51 | history | asked | Sebastien Palcoux | CC BY-SA 4.0 |