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The present essay provides a new metaphysical interpretation of Relational Quantum Mechanics (RQM) in terms of mereological bundle theory. The essential idea is to claim that a physical system in RQM can be defined as a mereological fusion…
Formalized $1$-category theory forms a core component of various libraries of mathematical proofs. However, more sophisticated results in fields from algebraic topology to theoretical physics, where objects have "higher structure," rely on…
In this paper we give a new proof of the Ne\v{s}et\v{r}il-R\"odl Theorem, a deep result of discrete mathematics which is one of the cornerstones of the structural Ramsey theory. In contrast to the well-known proofs which employ intricate…
Category theory provides a means through which many far-ranging fields of mathematics can be related by their similar structure. In a paper by Robinson [2], this interconnectivity afforded by categorical perspectives allowed for the…
We propose a generalization of Sullivan's de Rham homotopy theory to non-simply connected spaces. The formulation is such that the real homotopy type of a manifold should be the closed tensor dg-category of flat bundles on it much the same…
We prove that the category of (strictly unital) A$_\infty$-categories, linear over a commutative ring $R$, with strict A$_\infty$-morphisms has a cofibrantly generated model structure. In this model structure every object is fibrant and the…
We review the problem of finding a general framework within which one can construct quantum theories of non-standard models for space, or space-time. The starting point is the observation that entities of this type can typically be regarded…
Rough sets are approximations of concrete sets. The theory of rough sets has been used widely for data-mining. While it is well-known that adjunctions are underlying in rough approximations, such adjunctions are not enough for…
Locales have been studied as "topologies without points", mainly by tools of category theory. While traditional topology presents a space as a set of points with specified neighborhoods, localic topology presents a space as a lattice of…
In recent years philosophers of science have explored categorical equivalence as a promising criterion for when two (physical) theories are equivalent. On the one hand, philosophers have presented several examples of theories whose…
In this thesis we explore the questions of what should be considered a "classical" theory, and which aspects of quantum theory cannot be captured by any theory that respects our intuition of classicality. This exploration is divided in two…
Suppose one seeks to free oneself from a symmetric absolute space by quotienting out its symmetry group. This in general however fails to erase all memory of this absolute space's symmetry properties. Stratification is one major reason for…
The study of complex systems through the lens of category theory consistently proves to be a powerful approach. We propose that cognition deserves the same category-theoretic treatment. We show that by considering a highly-compact cognitive…
A realist interpretation of quantum mechanics is proposed - Contextual Quantum Realism (CQR) - according to which there exists a categorical distinction between the ideal (theory, observation instrument) and the real (quantum physical…
Unlike mathematics, in which the notion of truth might be abstract, in physics, the emphasis must be placed on algorithmic procedures for obtaining numerical results subject to the experimental verifiability. For, a physical science is…
We set out a fundamental ontology of atomism in terms of matter points. While being most parsimonious, this ontology is able to match both classical and quantum mechanics, and it remains a viable option for any future theory of cosmology…
We explore the possibility of replacing point set topology by higher category theory and topos theory as the foundation for quantum general relativity. We discuss the BC model and problems of its interpretation, and connect with the…
Modern data systems must support accountability across persistent legal, political, and analytic disagreement. This requirement imposes strict constraints on the design of any ontology intended to function as a shared substrate. We…
Existing work on quantum causal structure assumes that one can perform arbitrary operations on the systems of interest. But this condition is often not met. Here, we extend the framework for quantum causal modelling to situations where a…
The famous biologist Robert Rosen argued for an intrinsic difference between biological and artificial life, supporting the claim that `living systems are not mechanisms'. This result, understood as the claim that life-like mechanisms are…