Related papers: Why surplus structure is not superfluous
We address a recent proposal concerning 'surplus structure' due to Nguyen et al. ['Why Surplus Structure is Not Superfluous.' Br. J. Phi. Sci. Forthcoming.] We argue that the sense of 'surplus structure' captured by their formal criterion…
I consider two usages of the expression "gauge theory". On one, a gauge theory is a theory with excess structure; on the other, a gauge theory is any theory appropriately related to classical electromagnetism. I make precise one sense in…
We investigate structure that describes physical data in gravitational systems that is, to one degree or another, independent of the metric and affine structure. We dub such structure surplus structure and seek to incorporate it into our…
We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the…
This thesis is about conceptual aspects of gauge theories. Gauge theories lie at the heart of modern physics: in particular, they constitute the standard model of particle physics. At its simplest, the idea of gauge is that nature is best…
Gauge symmetries are often highlighted as a fundamental cornerstone of modern physics. But at the same time, it is commonly emphasized that gauge symmetries are not a fundamental feature of nature but merely redundancies in our description.…
The world appears to be well described by gauge theories; why? I suggest that gauge is more than mathematical redundancy. Gauge-dependent quantities can not be predicted, but there is a sense in which they can be measured. They describe…
We introduce a geometric construction of a gauge field theory of a complex adaptive system. It is based on a suitable simplicial formulation of a discrete geometry that manifests relevant properties valid in the classical differentiable…
Models of dependent type theories are contextual categories with some additional structure. We prove that if a theory $T$ has enough structure, then the category $T\text{-}\mathbf{Mod}$ of its models carries the structure of a model…
A-infinity algebras and categories are known to be the algebraic structures behind open string field theories. In this note we comment on the relevance of the homology construction of A-infinity categories to superpotentials.
In this paper, we present a review of the canonical structure of field theories defined on manifolds with time-like boundaries. The notion of differentiable generator is shown to be a requirement coming from the consistency of the…
Questions of set-theoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made…
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 formulation for a non-trivial composition of two classical gauge structures is given: Two parent gauge structures of a common base space are synthesized so as to obtain a daughter structure which is fundamental by itself. The model is…
Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater…
Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in…
Non-standard topics underlying a partly original approach to gauge field theory are concisely introduced, expressing ideas that were broached in several papers and, eventually, exposed in an organized form in a recently published book. By…
This note focuses the problem of motivating the use of gauge symmetries (being the identity on the observables) from general principles, beyond their practical success, starting from global gauge symmetries and then by emphasizing the…
We consider residue structures $R/G$ where $(G,+)$ is an additive subgroup of a ring $(R,+,\cdot)$, not necessarily an ideal. Special instances include Krasner's construction of quotient hyperfields, and Pumpluen's construction of…
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…