A new higher homotopy groupoid: the fundamental globular omega-groupoid of a filtered space

Covering morphisms of crossed complexes and of cubical omega-groupoids with connection are closed under tensor product

The aim is the theorems of the title and the corollary that the tensor product of two free crossed resolutions of groups or groupoids is also a free crossed resolution of the product group or groupoid. The route to this corollary is through the equivalence of the category of crossed complexes with that of cubical omega-groupoids with connections where the initial definition of the tensor product lies. It is also in the latter category that we are able to apply techniques of dense subcategories to identify the tensor product of covering morphisms as a covering morphism.

Batanin higher groupoids and homotopy types

We prove that any homotopy type can be recovered canonically from its associated weak omega-groupoid. This implies that the homotopy category of CW-complexes can be embedded in the homotopy category of Batanin's weak higher groupoids.

Quinn有限全同伦TQFT的范畴化及其在源自严格omega-群胚的TQFT与一次扩展TQFT中的应用

A categorification of Quinn's finite total homotopy TQFT with application to TQFTs and once-extended TQFTs derived from strict omega-groupoids

本文基于同伦理论重新审视并推广了Quinn的有限全同伦TQFT，提出了一种范畴化的一次扩展TQFT构造，适用于所有维度，并显式计算了同伦有限omega-群胚分类空间的情形，为离散高阶规范理论建模提供了工具。

Modelling and Computing Homotopy Types: I

The aim of this article is to explain a philosophy for applying higher dimensional Seifert-van Kampen Theorems, and how the use of groupoids and strict higher groupoids resolves some foundational anomalies in algebraic topology at the border between homology and homotopy. We explain some applications to filtered spaces, and special cases of them, while a sequel will show the relevance to n-cubes of pointed spaces.

Diagrammatic sets and rewriting in weak higher categories

We revisit Kapranov and Voevodsky's idea of spaces modelled on combinatorial pasting diagrams, now as a framework for higher-dimensional rewriting and the basis of a model of weak omega-categories. In the first part, we elaborate on Steiner's theory of directed complexes as a combinatorial foundation. We individuate convenient classes of directed complexes and develop the theory of diagrammatic sets relative to one such class. We study a notion of equivalence internal to a diagrammatic set, and single out as models of weak omega-categories those diagrammatic sets whose every composable diagram…

圆周上的余广群结构与Hodge退化

Cogroupoid structures on the circle and the Hodge degeneration

本研究发现拓扑圆周的E₂-余广群新结构，将非阿贝尔Hodge理论的Hodge退化解释为滤过环路空间E₂-广群的2重去环路化，关联了收缩映射、Todd类与有理同伦形式性，并给出Hochschild上同调层面的推论。