Timeline for Affine spaces as algebras for an operad?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 25, 2017 at 16:10 | answer | added | Vladimir Dotsenko | timeline score: 5 | |
| Jan 25, 2017 at 13:09 | comment | added | Karol Szumiło | The distinction between classical operads and cartesian operads that I describe in my answer is that in algebraic theories presented with operads you cannot insert "dummy variables". This means that you will not be able to identify affine combinations like $a x + b y$ and $a x + b y + 0 z$ since all identities in an operad need to have exactly the same set of variables on both sides. | |
| Jan 25, 2017 at 11:43 | answer | added | Karol Szumiło | timeline score: 6 | |
| Jan 25, 2017 at 10:43 | comment | added | Gabriel C. Drummond-Cole | For $K=\mathbb{R}$ the suboperad of positive $n$-tuples in $Pr_{\mathbb{R}}$ forms a natural suboperad of the little intervals operad (where the little intervals exhaust the big interval). | |
| Jan 25, 2017 at 7:21 | comment | added | მამუკა ჯიბლაძე | @QiaochuYuan Affine Lawvere theories have been investigated in the paper by Isbell, Klun and Schanuel | |
| Jan 25, 2017 at 5:34 | comment | added | Qiaochu Yuan | It feels more natural to me to describe this structure as an algebraic theory, or more formally as a Lawvere theory. It feels weird to me to describe it as an operad because I have no idea what algebras over it in non-cartesian monoidal categories ought to look like. | |
| Jan 25, 2017 at 5:20 | history | asked | Yuri Sulyma | CC BY-SA 3.0 |