Related papers: No categorial support for radical ontic structural…
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…
We present a new metaphysical framework for physics that is conceptually clear, ontologically parsimonious, and empirically adequate. This framework relies on the notion of self-subsisting structure, that is, a set of fundamental physical…
Reasoning about weak higher categorical structures constitutes a challenging task, even to the experts. One principal reason is that the language of set theory is not invariant under the weaker notions of equivalence at play, such as…
We show there exists a rigid monoidal category formed out by quantum linear spaces with an additional structure, such that FRT bialgebras and corresponding rectangular generalizations are its internal coEnd and coHom objects, respectively.…
In this mostly expository article, elements of higher category theory essential to the construction of a class of four dimensional quantum geometric models are reviewed. These models improve current state sum models for Quantum Gravity,…
A dialectical rough set theory focussed on the relation between roughly equivalent objects and classical objects was introduced in \cite{AM699} by the present author. The focus of our investigation is on elucidating the minimal conditions…
We develop foundations for oriented category theory, an extension of $(\infty,\infty)$-category theory obtained by systematic usage of the Gray tensor product, in order to study lax phenomena in higher category theory. As categorical…
In "Object generators, relaxed sets, and a foundation for mathematics", we introduced ``object generators'', a logical environment much more general than set theory. Inside this we found a `relaxed' version of set theory. That paper is…
According to Relational Quantum Mechanics (RQM) the wave function $\psi$ is considered neither a concrete physical item evolving in spacetime, nor an object representing the absolute state of a certain quantum system. In this interpretative…
Recent work in set theory indicates that there are many different notions of 'set', each captured by a different collection of axioms, as proposed by J. Hamkins in [Ham11]. In this paper we strive to give one class theory that allows for a…
This paper investigates some issues arising in categorical models of reversible logic and computation. Our claim is that the structural (coherence) isomorphisms of these categorical models, although generally overlooked, have decidedly…
We define realism using a slightly modified version of the EPR criterion of reality. This version is strong enough to show that relativity is incomplete. We show that this definition of realism is nonetheless compatible with the general…
I argue that spacetime singularities entail no ontological commitment to material entities. First, I show that Penrose's singularity theorem is best understood as a theorem of incompleteness, it demonstrates the failure of specific…
We develop a categorical framework for reasoning about abstract properties of differentiation, based on the theory of fibrations. Our work encompasses the first-order fragments of several existing categorical structures for differentiation,…
Relational Quantum Mechanics (RQM) is an interpretation of quantum theory based on the idea of abolishing the notion of absolute states of systems, in favor of states of systems relative to other systems. Such a move is claimed to solve the…
The ordinary Structure Identity Principle states that any property of set-level structures (e.g., posets, groups, rings, fields) definable in Univalent Foundations is invariant under isomorphism: more specifically, identifications of…
In this paper, we have studied the axiomatics of {\it Ann-categories} and {\it categorical rings.} These are the categories with distributivity constraints whose axiomatics are similar with those of ring structures. The main result we have…
This paper investigates the mathematical and philosophical foundations of relational observables and reference frames using the fibre bundle formalism. Two paradigms are contrasted: the View from Nowhere, which interprets frame-dependent…
We show that in the category of preordered sets, there is a natural notion of pretorsion theory, in which the partially ordered sets are the torsion-free objects and the sets endowed with an equivalence relation are the torsion objects.…
We reconstruct finite-dimensional quantum theory from categorical principles. That is, we provide properties ensuring that a given physical theory described by a dagger compact category in which one may `discard' objects is equivalent to a…