In order to execute database queries eeciently, they are usually translated into an algebra: a small set of operations together with some equivalences. The operations are implemented very eeciently by the database engine, and the equivalences are used to optimise the query. Since query languages for object-oriented databases are more complex than their relational counterparts , the algebra and ...

Introduction 2 1. Symmetric spectra 5 1.1. Simplicial sets 5 1.2. Symmetric spectra 6 1.3. Simplicial structure on Sp 8 1.4. Symmetric Ω-spectra 10 2. The smash product of symmetric spectra 11 2.1. Symmetric sequences 11 2.2. Symmetric spectra 14 2.3. The ordinary category of spectra 18 3. Stable homotopy theory of symmetric spectra 19 3.1. Stable equivalence 20 3.2. Model categories 26 3.3. Le...

Abstract We investigate maximal tori in the Hochschild cohomology Lie algebra ${\operatorname {HH}}^1(A)$ of a finite dimensional $A$, and their connection with fundamental groups associated to presentations $A$. prove that every torus arises as dual some group extending work by Farkas, Green, Marcos; de la Peña Saorín; Le Meur. Combining this known invariance results for cohomology, we deduce ...

In this paper we propose an approach to homotopical algebra where the basic ingredient is a category with two classes of distinguished morphisms: strong and weak equivalences. These data determine the cofibrant objects by an extension property analogous to the classical lifting property of projective modules. We define a Cartan-Eilenberg category as a category with strong and weak equivalences ...

The aim of the paper is to give a formal compositional semantics for Spiking Neural P systems (SNP systems) by following the Structural Operational Semantics (SOS) approach. A process algebra is introduced whose terms represent SNP systems. The algebra is equipped with a semantics, given as a labelled transition system. This semantics allows notions of behavioural equivalences over SNP systems ...

We study several process equivalences on a probabilistic process algebra. First, we define an operational semantics. Afterwards we introduce the notion of passing a test with a probability. We consider three families of tests according to the intended behavior of an external observer: Reactive (sequential tests), generative (branching tests), and limited generative (equitable branching tests). ...

The class of shape equivalences for a pair (C,K) of categories is the orthogonal of K, that is Σ = K. Then Σ is internally saturated (Σ = Σ). On the other hand, every internally saturated class of morphisms Σ ⊂ Mor(C), is the class of shape equivalences for some pair (C,K). Moreover, every class of shape equivalences Σ enjoys a calculus of left fractions and such a fact allows one to use techni...

We establish a large class of homotopy coherent Morita-equivalences Dold-Kan type relating diagrams with values in any weakly idempotent complete additive $\infty$-category; the guiding example is an $\infty$-categorical correspondence between $\infty$-categories simplicial objects and connective chain complexes. Our results generalize many known 1-categorical equivalences such as classical cor...