论文标题
TQ-Completion和身份函子的泰勒塔
TQ-completion and the Taylor tower of the identity functor
论文作者
论文摘要
这篇简短论文的目的是研究在光谱中的大型代数的背景下，身份函数的泰勒塔的融合。具体来说，我们表明，如果$ a $是$（ - 1）$ - 连接的$ \ Mathcal {o} $ - 代数，带有$ 0 $ - 连接的$ \ Mathsf {tq} $ - 同源性频谱$ \ Mathsf {tq}（tq}（tq}（a）） a_ \ mathsf {tq}^\ wedge $介于以$ a $和$ \ mathsf {tq} $ $ a $ a $的$ a $和$ \ mathsf {tq} $上评估的身份函数的限制之间。由于在这种情况下，身份函数仅是$ 0 $ - 分析，因此该结果将对身份的泰勒塔的知识扩展到其“收敛半径”之外。
The goal of this short paper is to study the convergence of the Taylor tower of the identity functor in the context of operadic algebras in spectra. Specifically, we show that if $A$ is a $(-1)$-connected $\mathcal{O}$-algebra with $0$-connected $\mathsf{TQ}$-homology spectrum $\mathsf{TQ}(A)$, then there is a natural weak equivalence $P_\infty$(id)$A\simeq A_\mathsf{TQ}^\wedge$ between the limit of the Taylor tower of the identity functor evaluated on $A$ and the $\mathsf{TQ}$-completion of $A$. Since, in this context, the identity functor is only known to be $0$-analytic, this result extends knowledge of the Taylor tower of the identity beyond its "radius of convergence."
