Related papers: Why Not Categorical Equivalence?
The work argues the principle of equivalence to be a theorem and not a principle (in a sense of an axiom). It contains a detailed analysis of the concepts of normal and inertial frame of reference. The equivalence principle is proved to be…
Epistemic uncertainty arises in lack of complete knowledge about the state of a system. There are multiple mathematical frameworks for measuring such uncertainty quantitatively, often referred to as imprecise probability theories. Inspired…
In categorical realizability, it is common to construct categories of assemblies and categories of modest sets from applicative structures. These categories have structures corresponding to the structures of applicative structures. In the…
Do correctness and completeness of quantum mechanics jointly imply that quantum state vectors are necessarily in one-to-one correspondence with elements of the physical reality? In terms of category theory, such a correspondence would stand…
This document is centered around a main idea: simplicial categories, by which we mean simplicial objects in the category of categories, can be treated as a two-fold categorical structure and their double category theory is homotopically…
While many different models for $(\infty,1)$-categories are currently being used, it is known that they are Quillen equivalent to one another. Several higher-order analogues of them are being developed as models for $(\infty,…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
The generality and pervasiness of category theory in modern mathematics makes it a frequent and useful target of formalization. It is however quite challenging to formalize, for a variety of reasons. Agda currently (i.e. in 2020) does not…
Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only incorporates the data of the desired objects, but also…
The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful;…
This paper proposes a formal cognitive framework for problem solving based on category theory. We introduce cognitive categories, which are categories with exactly one morphism between any two objects. Objects in these categories are…
I provide a critical commentary regarding the attitude of the logician and the philosopher towards the physicist and physics. The commentary is intended to showcase how a general change in attitude towards making scientific inquiries can be…
In a recent paper by the author, a new approach was suggested for quantising space-time, or space. This involved developing a procedure for quantising a system whose configuration space--or history-theory analogue--is the set of objects in…
I give a pedagogical explanation of what it is about quantization that makes general relativity go from being a nearly perfect classical theory to a very problematic quantum one. I also explain why some quantization of gravity is…
The long lasting discussion on the completeness of quantum theory (QT) has not yet come to an end. The discussion is impeded by the lack of a clear understanding of what makes up the contents of a theory of physics in general and of QT…
In the literature, there have been several methods and definitions for working out if two theories are "equivalent" (essentially the same) or not. In this article, we do something subtler. We provide means to measure distances (and explore…
Already in the 1970s there where attempts to present a set of ground rules, sometimes referred to as a theory of gravitation theories, which theories of gravity should satisfy in order to be considered viable in principle and, therefore,…
The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and…
We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…
Most of the approaches to the construction of a theory of quantum gravity share some principles which do not have specific experimental support up to date. Two of these principles are relevant for our discussion: (i) the gravitational field…