相关论文: The club of simplicial sets

We introduce a notion of join for (augmented) simplicial sets generalising the classical join of geometric simplicial complexes. The definition comes naturally from the ordinal sum on the base simplicial category $\Delta$.

This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…

We give a general notion of combinatory completeness with respect to a faithful cartesian club and use it systematically to obtain characterisations of a number of different kinds of applicative system. Each faithful cartesian club…

The notion of a simplicial set originated in algebraic topology, and has also been utilized extensively in category theory, but until relatively recently was not used outside of those fields. However, with the increasing prominence of…

We give a definition of associative schemes, schemes of associative rings, over a field $k,$ using the definition of completion of an associative $k$-algebra in a finite set of simple modules. We start by giving a weaker but sufficient…

We explain how the simplicial higher-order unstable homotopy operations defined in [BBS2] may be composed and inserted one in another, thus forming a coherent if complicated algebraic structure.

Both simplicial sets and simplicial spaces are used pervasively in homotopy theory as presentations of spaces, where in both cases we extract the "underlying space" by taking geometric realization. We have a good handle on the category of…

We show that the nerve of a strict omega-category can be described algebraically as a simplicial set with additional operations subject to certain identities. The resulting structures are called sets with complicial identities. We also…

We develop a cohomological method to classify amalgams of groups. We generalize this to simplicial amalgams in any concrete category. We compute the non-commutative 1-cohomology for several examples of amalgams defined over small simplices.

A discrete (finite-difference) analogue of differential forms is considered, defined on simplicial complexes, including triangulations of continuous manifolds. Various operations are explicitly defined on these forms, including exterior…

This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins. It is intended to be accessible to…

We develop a structure theory of connected solvable spherical subgroups in semisimple algebraic groups. Based on this theory, we obtain an explicit classification of all such subgroups up to conjugation.

We give a new construction of the Joyal model structure on the category of simplicial sets, and we provide a simple characterization of the fibrations in it. We characterize the inner anodyne maps in terms of categorical equivalences and…

We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…

A group, defined as set with associative multiplication and inverse, is a natural structure describing the symmetry of a space. The concept of group generalizes to group objects internal to other categories than sets. But there are yet more…

We set up a general framework for enriching a subcategory of the category of noncommutative sets over a category C using products of the objects of a non-\Sigma operad P in \C. By viewing the simplicial category as a subcategory of the…

Algebraic structures such as monoids, groups, and categories can be formulated within a category using commutative diagrams. In many common categories these reduce to familiar cases. In particular, group objects in Grp are abelian groups,…

We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the set of parameters.

In this paper we construct a cofibrantly generated model category structure on the category of all small symmetric multicategories enriched in simplicial sets.

Let $A$ be either a simplicial complex $K$ or a small category $\mathcal C$ with $V(A)$ as its set of vertices or objects. We define a twisted structure on $A$ with coefficients in a simplicial group $G$ as a function $$ \delta\colon…