A Discrete Model of S-homotopy Theory
نویسنده
چکیده
Abstract. We construct a discrete model of the homotopy theory of S-spaces. We define a category P with objects composed of a simplicial set and a cyclic set along with suitable compatibility data. P inherits a model structure from the model structures on the categories of simplicial sets and cyclic sets. We then show that there is a Quillen equivalence between P and the model category of S-spaces in which weak equivalences and fibrations are maps inducing weak equivalences and fibrations on passage to all fixed point sets.
منابع مشابه
A Short Note on Models for Equivariant Homotopy Theory
These notes explore equivariant homotopy theory from the perspective of model categories in the case of a discrete group G. Section 2 reviews the situation for topological spaces, largely following [May]. In section 3, we discuss two approaches to equivariant homotopy theory in more general model categories. Section 4 discusses some examples to which the material from Section 3 applies. In part...
متن کاملHomotopy Meaningful Hybrid Model Structures
Hybrid systems are systems that display both discrete and continuous behavior and, therefore, have the ability to model a wide range of robotic systems such as those undergoing impacts. The main observation of this paper is that systems of this form relate in a natural manner to very special diagrams over a category, termed hybrid objects. Using the theory of model categories, which provides a ...
متن کاملUnivalent polymorphism
We show that Martin Hyland's effective topos can be exhibited as the homotopy category of a path category $\mathbb{EFF}$. Path categories are categories of fibrant objects in the sense of Brown satisfying two additional properties and as such provide a context in which one can interpret many notions from homotopy theory and Homotopy Type Theory. Within the path category $\mathbb{EFF}$ one can i...
متن کاملMODELLING AND ANALYSIS OF A DISCRETE-TIME PRIORITY QUEUING COMPUTER NETWORK WITH PRIORITY JUMPS USING PROBABILITY GENERATING FUNCTIONS
Priority queues have a great importance in the study of computer communication networks in which different types of traffic require different quality of service standards. The discrete-time non-preemptive priority queuing model with priority jumps is proposed in this paper. On the basis of probability generating functions mean system contents and mean queuing delay characteristics are obtained....
متن کاملMaster Thesis Elmendorf’s Theorem for Cofibrantly Generated Model Categories
Elmendorf’s Theorem in equivariant homotopy theory states that for any topological group G, the model category of G-spaces is Quillen equivalent to the category of continuous diagrams of spaces indexed by the opposite of the orbit category of G with the projective model structure. For discrete G, Bert Guillou explored equivariant homotopy theory for any cofibrantly generated model category C an...
متن کامل