Related papers: Parametrized K-Theory
We define a notion of formal quantum field theory and associate a formal quantum field theory to K-theoretical intersection theories on Hilbert schemes of points on algebraic surfaces. This enables us to find an effective way to compute…
The concept of category from mathematics happens to be useful to computer programmers in many ways. Unfortunately, all "good" explanations of categories so far have been designed by mathematicians, or at least theoreticians with a strong…
Matching logic is a general formal framework for reasoning about a wide range of theories, with particular emphasis on programming language semantics. Notably, the intermediate language of the K semantics framework is an extension of…
It is shown that the K-theory of every noetherian base scheme of finite Krull dimension is represented by a strict ring object in the setting of motivic stable homotopy theory. The adjective `strict' is used to distinguish between the type…
This brief brochure is intended to present a philosophical theory known as relational materialism. We introduce the postulates and principles of the theory, articulating its ontological and epistemological content using the language of…
We consider a finite universe U (more exactly - a family U of them) and second order quantifiers Q_K, where for each U this means quantifying over a family of n(K)-place relations closed under permuting U. We define some natural orders and…
These notes provide an introduction to the theory of localization for triangulated categories. Localization is a machinery to formally invert morphisms in a category. We explain this formalism in some detail and we show how it is applied to…
In this paper, we give an overview of some recent work on applying tools from category theory in finite model theory, descriptive complexity, constraint satisfaction, and combinatorics. The motivations for this work come from Computer…
We unite elements of category theory, K-theory, and geometric group theory, by defining a class of groups called $k$-cube groups, which act freely and transitively on the product of $k$ trees, for arbitrary $k$. The quotient of this action…
This paper formulates a notion of independence of subobjects of an object in a general (i.e. not necessarily concrete) category. Subobject independence is the categorial generalization of what is known as subsystem independence in the…
We adapt Quillen's calculation of graded K-groups of Z-graded rings with support in N to graded K-theory, allowing gradings in a product Z \times G with G an arbitrary group. This in turn allows us to use inductions and calculate graded…
Generalized differential cohomology theories, in particular differential K-theory (often called "smooth K-theory"), are becoming an important tool in differential geometry and in mathematical physics. In this survey, we describe the…
We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it changes under the influence of the rest of the universe. Therefore…
Category theory has become central to certain aspects of theoretical physics. Bain [Synthese, 190:1621--1635 (2013)] has recently argued that this has significance for ontic structural realism. We argue against this claim. In so doing, we…
The Farrell-Jones and the Baum-Connes Conjecture say that one can compute the algebraic K- and L-theory of the group ring and the topological K-theory of the reduced group C^*-algebra of a group G in terms of these functors for the…
We derive the category-theoretic backbone of quantum theory from a process ontology. More specifically, we treat quantum theory as a theory of systems, processes and their interactions. In this first part of a three-part overview, we first…
Life continuously changes its own components and states at each moment through interaction with the external world, while maintaining its own individuality in a cyclical manner. Such a property, known as "autonomy," has been formulated…
In analogy with the classical theory of topological groups, for finitely complete categories enriched with Grothendieck topologies, we provide the concepts of localized G-topological space, initial Grothendieck topologies and continuous…
Controlled $K$-theory is used to show that algebraic $K$-theory of virtually abelian groups is described by an assembly map defined using possibly-infinite hyperelementary subgroups. The Farrell-Jones summand (coming from infinite…
The goal of this paper is to summarise the first steps in developing a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum…