Timeline for Animated rings and $\mathbb E_{\infty}$-rings
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 1 at 10:44 | comment | added | Z. M | No, the left adjoint is $\DeclareMathOperator\An{An}\An\DeclareMathOperator\CAlg{CAlg}\DeclareMathOperator\cn{cn}\DeclareMathOperator\an{an}\to\CAlg_R^{\an}\to\CAlg_R^{E_\infty,\cn}$ which carries a finite set to the polynomial $R$-algebra generated by this finite set and then to the free $E_\infty$-$R$-algebra generated by this finite set. | |
| May 1 at 10:41 | comment | added | Y.M | So it should be the left adjoint takes free $E_{\infty}$-$R$-algebras to poly $R$-algebras? | |
| May 1 at 10:34 | comment | added | Z. M | @Y.M The left adjoint carries free objects to free objects: consider taking left adjoints of the forgetful functor from animated rings to connective $E_\infty$-rings and then to anima. | |
| May 1 at 10:16 | comment | added | Y.M | Thanks for the answer. In the proof of Prop 1, what do you mean by saying the left adjoint carries poly $R$-algebras to free $E_{\infty}$-$R$-algebras? My original concern is how to compare $Map(A,B)$ and $Map(A,\Theta(B))$ with $A$ a discrete $R$-algebra and $B$ an animated $R$-algebra. So I guess there is no general way to compare them? | |
| May 1 at 9:04 | history | answered | Z. M | CC BY-SA 4.0 |