Related papers: Categorical Generalization and Physical Structural…
The representations of the world around in physics built with help of causality are analyzed and seems incomplete. The observer's causal representations form a closed logical system, i.e. the compact group related to cause-effect chains.…
We introduce a formalism based on a combinatorial notion of cell complex subject to an inclusion-reversing duality operation. Our main goal is to open the way for a functorial definition of field theories in a context where no manifold or…
Recently discovered domain-specific formal systems -- specifically homotopy type theory and simplicial type theory -- provide new perspectives on spaces and categories in a natively equivalence-invariant setting. In this note, we expose…
We consider (finitary, propositional) logics through the original use of Category Theory: the study of the "sociology of mathematical objects", aligning us with a recent, and growing, trend of study logics through its relations with other…
A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…
Recent work by physicists on gravity in two dimensions has a natural generalization to four dimensions, formulated in terms of an analogue of Segal's category [defined for the study of conformal field theory].
Based on a clear ontology of material individuals, we analyze in detail the factual semantics of quantum theory, and argue that the basic mathematical formalism of quantum theory is just okay with (a certain form of ) realism and that it is…
It was recently suggested that causal structures are both dynamical, because of general relativity, and indefinite, due to quantum theory. The process matrix formalism furnishes a framework for quantum mechanics on indefinite causal…
Compact categories have lately seen renewed interest via applications to quantum physics. Being essentially finite-dimensional, they cannot accomodate (co)limit-based constructions. For example, they cannot capture protocols such as quantum…
fc-multicategories are a very general kind of two-dimensional structure, encompassing bicategories, monoidal categories, double categories and ordinary multicategories. We define them and explain how they provide a natural setting for two…
We investigate an enriched-categorical approach to a field of discrete mathematics. The main result is a duality theorem between a class of enriched categories (called $\overline{\mathbb{Z}}$- or $\overline{\mathbb{R}}$-categories) and that…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
We give a short introduction to category theory aimed at philosophers. We emphasize methodological issues and philosophical ramifications.
Machine learning models rely on various assumptions to attain high accuracy. One of the preliminary assumptions of these models is the independent and identical distribution, which suggests that the train and test data are sampled from the…
We specialise a recently introduced notion of generalised dinaturality for functors $T : (\mathcal{C}^\text{op})^p \times \mathcal{C}^q \to \mathcal{D}$ to the case where the domain (resp., codomain) is constant, obtaining notions of ends…
This text is dedicated to the development of the theory of $(\infty,\omega)$-categories. We present generalizations of standard results from category theory, such as the lax Grothendieck construction, the Yoneda lemma, lax (co)limits and…
Approaching limitations of digital computing technologies have spurred research in neuromorphic and other unconventional approaches to computing. Here we argue that if we want to systematically engineer computing systems that are based on…
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
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,…
The paper offers an argument against an intuitive reading of the Stone-von Neumann theorem as a categoricity result, thereby pointing out that, against what is usually taken to be the case, this theorem does not entail any model-theoretical…