发表机构
Universidade Federal do Paraná; Philipps-Universität Marburg（巴拉那联邦大学; 马尔堡菲利普大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为拓扑着色非对称操作子构造CW同伦操作子及严格CW操作子的同伦同构，并推广至拓扑代数与有限CW复形图，增强Quillen伴随并嵌入预层范畴。
AI 中文摘要
在本文中，对于每个具有CW空间的各元拓扑着色非对称操作子，我们构造一个与CW同伦操作子（即所有高阶同伦相对于乘积结构和立方体上的CW结构都是胞腔的）的同伦同构，且不改变其对象。通过使用双侧杠构造，我们将其修正为与严格CW操作子的同伦同构。这更一般地适用于集合上着色操作子上的拓扑代数。在有限偏序集上的有限CW复形图的情形下，所得图由有限CW空间组成，增强了单纯集合与拓扑空间之间的Quillen伴随。作为副产品，我们将操作子上的拓扑同伦代数嵌入到$P$-树范畴的分支消解上的预层范畴中，推广了拓扑操作子的已知情形。
英文摘要
In this note, for every topological colored nonsymmetric operad with CW spaces in each arity we construct a homotopy isomorphism with a CW homotopy operad (i.e. all higher homotopies are cellular with respect to the product structure and CW structure on cubes) not changing its objects. By using the two-sided bar construction, we rectify this to a homotopy isomorphism with a strict CW operad. This applies more generally to topological algebras over colored operads in sets. In the case of diagrams of finite CW complexes over finite posets, the resulting diagram consists of finite CW spaces enhancing the Quillen adjunction between simplicial sets and topological spaces. As a byproduct, we produce an embedding of topological homotopy algebras over operads into the presheaf category over the branch resolution for the category of $P$-trees generalizing the known case of topological operads.
Comments24 pages, 5 figures; comments are welcome
