Joins for (Augmented) Simplicial Sets

圆柱与细分的半单纯组合学

Semi-simplicial combinatorics of cyclinders and subdivisions

本文通过余半单纯集作用与序列基数函子，统一分析增广半单纯集的圆柱与细分，并借助二项式、斯特林数等矩阵计算单纯形数量，揭示几何与代数背景的联系。

The Symmetric Join Operad

The join operad arises from the combinatorial study of the iterated join of simplices. We study a suitable simplicial version of this operad which includes the symmetries given by permutations of the factors of the join. From this combinatorics we construct an E-infinity operad which coacts naturally on the chains of a simplicial set.

Abstract cellularization as a cellularization with respect to a set of objects

Given a simplicial idempotent augmented endofunctor $F$ on a simplicial combinatorial model category $M$, under the assumption of Vopenka's principle, we exhibit a set $A$ of cofibrant objects in $M$ such that $F$ is equivalent to $\CW_A$, the cellularization with respect to $A$.

简短的新Dowker对偶性证明

Short, new proofs of Dowker duality

本文通过三种简短新方法证明Dowker对偶性，引入了关系连接和关系积复形，展示了 simplicial 复形与关系复形的同调在长正合列中相互关联。

Weak complicial sets, a simplicial weak omega-category theory. Part I: basic homotopy theory

This paper develops the foundations of a simplicial theory of weak omega-categories, which builds upon the insights originally expounded by Ross Street in his 1987 paper on oriented simplices. The resulting theory of weak complicial sets provides a common generalisation of the theories of (strict) omega-categories, Kan complexes and Joyal's quasi-categories. We generalise a number of results due to the current author with regard to complicial sets and strict omega-categories to provide an armoury of well behaved technical devices, such as joins and Gray tensor products, which will be used to s…