论文标题
在结构化环光谱中的身份的善意衍生物上
On the Goodwillie derivatives of the identity in structured ring spectra
论文作者
论文摘要
The aim of this paper is three-fold: (i) we construct a naturally occurring highly homotopy coherent operad structure on the derivatives of the identity functor on structured ring spectra which can be described as algebras over an operad $\mathcal{O}$ in spectra, (ii) we prove that every connected $\mathcal{O}$-algebra has a naturally occurring left action of the derivatives of the身份，（iii）我们表明，在$ \ Mathcal {O} $ - 代数 - 代数和oprad $ \ Mathcal {o} $之间，高度同质相干作战天然存在较弱的等效性。 在此过程中，我们介绍了$ \ Mathbf {n} $ - 彩色的彩色作业的概念，其级别（通过构造）提供了一个精确的代数框架，用于与高度同型相干，作战，作战及其代数合作和比较。
The aim of this paper is three-fold: (i) we construct a naturally occurring highly homotopy coherent operad structure on the derivatives of the identity functor on structured ring spectra which can be described as algebras over an operad $\mathcal{O}$ in spectra, (ii) we prove that every connected $\mathcal{O}$-algebra has a naturally occurring left action of the derivatives of the identity, and (iii) we show that there is a naturally occurring weak equivalence of highly homotopy coherent operads between the derivatives of the identity on $\mathcal{O}$-algebras and the operad $\mathcal{O}$. Along the way, we introduce the notion of $\mathbf{N}$-colored operads with levels which -- by construction -- provides a precise algebraic framework for working with and comparing highly homotopy coherent operads, operads, and their algebras.
