Abstract Given a group G and -category $${\textbf{C}}$$ C , we give condition on diagram of simplicial sets indexed by that allows us to define natural action its homotopy colimit, some other defined in terms the diagram. Well-known theorems homeomorphisms equivalences are generalized equivariant versions.

We study diagrams associated with a finite simplicial complex K, in various algebraic and topological categories. We relate their colimits to familiar structures in algebra, combinatorics, geometry and topology. These include: right-angled Artin and Coxeter groups (and their complex analogues, which we call circulation groups); Stanley-Reisner algebras and coalgebras; Davis and Januszkiewicz's ...

Colimits are a powerful tool for the combination of objects in a category. In the context of modeling and specification, they are used in the institution-independent semantics (1) of instantiations of parameterised specifications (e.g. in the specification language CASL), and (2) of combinations of networks of specifications (in the OMG standardised language DOL). The problem of using colimits ...

That is, maps from A to B∗ are given by integral kernels in (A⊗B)∗. However, the validity of this adjunction depends on existence of a genuine tensor product. We recall in an appendix the demonstration that infinitedimensional Hilbert spaces do not have tensor products. Also, we must specify the topology on the duals B∗ and (A⊗B)∗. The strongest conclusion gives these the strong topology, as co...

We construct an analogue of the normaliser decomposition for p–local finite groups (S,F ,L) with respect to collections of F –centric subgroups and collections of elementary abelian subgroups of S . This enables us to describe the classifying space of a p–local finite group, before p–completion, as the homotopy colimit of a diagram of classifying spaces of finite groups whose shape is a poset a...

We define a construction operation on hypergraphs using a colimit and show that its expressiveness concerning graph rewriting is equal to the graph expressions of Courcelle and the double-pushout approach of Ehrig. With an inductive way of representing graphs, graph rewriting arises naturally as a derived concept. The usefulness of our approach for the compositional modelling of concurrent syst...

A model theory of a typed, declarative, temporal object-oriented language system is presented. The declarative nature of the language makes it very different from the dominating procedural, strongly typed object-oriented programming languages. In this declarative system, methods are specified in a high-level, temporal constraint language. Two fundamental properties of these constraints are that...

We define a monad on the category of complete metric spaces with short maps, which assigns to each space the space of Radon probability measures on it with finite first moment, equipped with the Kantorovich–Wasserstein distance. It is analogous to the Giry monad on the category of Polish spaces, and it extends a construction due to van Breugel for compact and for 1bounded complete metric spaces...

In this paper we develop homotopy theoretical methods for studying diagrams. In particular we explain how to construct homotopy colimits and limits in an arbitrary model category. The key concept we introduce is that of a model approximation. A model approximation of a category C with a given class of weak equivalences is a model category M together with a pair of adjoint functors M ⇄ C which s...

We define a notion of cosheaves on diffeological spaces by cosheaves on the site of plots. This provides a framework to describe diffeological objects such as internal tangent bundles, the Poincar'{e} groupoids, and furthermore, homology theories such as cubic homology in diffeology by the language of cosheaves. We show that every cosheaf on a diffeological space induces a cosheaf in terms of t...