Related papers: Quotient Categories and Phases
There are many ways to present model categories, each with a different point of view. Here we'd like to treat model categories as a way to build and control resolutions. This an historical approach, as in his original and spectacular…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
We generalize the small object argument in order to allow for its application to proper classes of maps (as opposed to sets of maps in Quillen's small object argument). The necessity of such a generalization arose with appearance of several…
We provide a complete answer to the question "When is a quotient of a Leavitt path algebra isomorphic to a Leavitt path algebra?" in terms of the interaction of the kernel of the quotient homomorphism with the cycles of the digraph. A key…
This paper develops a basic theory of H-groups. We introduce a special quotient of H-groups and extend some algebraic constructions of topological groups to the category of H-groups and H-maps. We use these constructions to prove some…
The notion of locality semigroups was recently introduced with motivation from locality in convex geometry and quantum field theory. We show that there is a natural correspondence between locality sets and quivers which leads to a concrete…
We introduce the quantum isomeric supercategory and the quantum affine isomeric supercategory. These diagrammatically defined supercategories, which can be viewed as isomeric analogues of the HOMFLYPT skein category and its affinization,…
The theory of $N$-complexes is a generalization of both ordinary chain complexes and graded objects. Hence it yields deeper insight in the structure of these and offers a broader range of applications. This work generalizes the tensor…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…
We axiomatise the dagger category of complex Hilbert spaces and bounded linear maps, using exclusively purely categorical conditions. Our axioms are chosen with the aim of an easy interpretability: two of them describe the composition of…
We define the category $\mathcal{QM}$ of quantales and their modules and prove the existence of coproducts, and the one of pushout and amalgamated coproducts under certain conditions. Then we define the non-full subcategory…
To any finite group G in SL_2(C), and each `t' in the center of the group algebra of G, we associate a category, Coh_t. It is defined as a suitable quotient of the category of graded modules over (a graded version of) the deformed…
We describe all the localization observables of a quantum particle in a one-dimensional box in terms of sequences of unit vectors in a Hilbert space. An alternative representation in terms of positive semidefinite complex matrices is…
Covariational reasoning--considering how changes in one quantity affect another, related quantity--is a foundation of quantitative modeling in physics. Understanding quantitative models is a learning objective of introductory physics…
We introduce a new cubical model for homotopy types. More precisely, we'll define a category Qs with the following features: Qs is a PROP containing the classical box category as a subcategory, the category Qs-Set of presheaves of sets on…
Classically general covariance is found from the idea that a vector is a physical quantity which exists independently of choice of coordinate system and is unchanged by a change of coordinate system. It is often assumed that there exists…
In a bicategory of spans (an example of a 'generic bicategory') the factorization of a span (s,t) as the span (s,1) followed by (1,t) satisfies a simple universal property with respect to all factorizations in terms of the generic…
In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also…
We revisit the definition of Cartesian differential categories, showing that a slightly more general version is useful for a number of reasons. As one application, we show that these general differential categories are comonadic over…
Many insights into the quantum world can be found by studying it from amongst more general operational theories of physics. In this thesis, we develop an approach to the study of such theories purely in terms of the behaviour of their…