Timeline for Classification of the functors on the category of cyclic groups
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Feb 2, 2020 at 6:29 | history | edited | Sebastien Palcoux | CC BY-SA 4.0 |
bonus question
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| Jan 31, 2020 at 13:25 | history | became hot network question | |||
| Jan 31, 2020 at 11:57 | comment | added | Martin Brandenburg | The first question is answered by Neil below, the second: the tensor product of abelian groups. We have $C_n \otimes C_m = C_{\mathrm{gcd}(n,m)}$ for $n,m \geq 0$. | |
| Jan 31, 2020 at 11:45 | comment | added | Sebastien Palcoux | @MartinBrandenburg: Which bifunctor provides a symmetric monoidal structure? | |
| Jan 31, 2020 at 11:43 | comment | added | Sebastien Palcoux | @MartinBrandenburg Is there a non-constant functor $F$ with $F(C_1) \neq C_1$? | |
| Jan 31, 2020 at 10:38 | comment | added | Martin Brandenburg | Another remark: $\mathsf{Cyc}$ has at least two additional structures, for example it is $\mathbb{Z}$-linear (aka preadditive) and symmetric monoidal. It is much easier to classify the functors which preserves one of both of these structures. | |
| Jan 31, 2020 at 10:32 | comment | added | Martin Brandenburg | The first step is to describe the morphisms in $\mathsf{Cyc}$ by generators and relations and thereby to give a description of functors into any category. But it will be quite complicated and not easy to simplify even for simple target categories. | |
| Jan 31, 2020 at 10:26 | comment | added | Martin Brandenburg | I think that there are too many functors to classify them. | |
| Jan 31, 2020 at 9:55 | answer | added | Neil Strickland | timeline score: 9 | |
| Jan 31, 2020 at 9:10 | history | edited | Sebastien Palcoux | CC BY-SA 4.0 |
we can say a bit more
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| Jan 31, 2020 at 5:15 | history | asked | Sebastien Palcoux | CC BY-SA 4.0 |