Related papers: Insights From Univalent Foundations: A Case Study …
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…
In this paper we show how the theory of monads can be used to deduce in a uniform manner several duality theorems involving categories of relations on one side and categories of algebras with homomorphisms preserving only some operations on…
We introduce a foundational sheaf theoretical scheme for the comprehension of quantum event structures, in terms of localization systems consisting of Boolean coordinatization coverings induced by measurement. The scheme is based on the…
A co-valuation is, essentially, a minimal finite cover. We introduce a logic based on co-valuations, which play the role of valuations of free variables in classical first-order logic, and show that the fundamental tools of model theory --…
Written to be contributed as the "mathematical modeling" chapter of a book, edited by Elaine Landry, to be titled "Categories for the Working Philosopher". In this chapter, category theory is presented as a mathematical modeling framework…
This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the…
Quantum computing has been a fascinating research field in quantum physics. Recent progresses motivate us to study in depth the universal quantum computing models (UQCM), which lie at the foundation of quantum computing and have tight…
This thesis is devoted to algorithmic aspects of the implementation of Cartan's moving frame method to the problem of the equivalence of submanifolds under a Lie group action. We adopt a general definition of a moving frame as an…
We propose Universal Causality, an overarching framework based on category theory that defines the universal property that underlies causal inference independent of the underlying representational formalism used. More formally, universal…
In this article we present a new modelling framework for structured concepts using a category-theoretic generalisation of conceptual spaces, and show how the conceptual representations can be learned automatically from data, using two very…
In this monograph we provide an in-depth and systematic study of pseudolimits of pseudofunctors $F:\mathscr{C}^{op} \to \mathfrak{Cat}$ in the $2$-category of categories where $\mathscr{C}$ is a $1$-category and use this to give an explicit…
The concept of process is ubiquitous in science, engineering and everyday life. Category theory, and monoidal categories in particular, provide an abstract framework for modelling processes of many kinds. In this paper, we concentrate on…
Category theory is famous for its innovative way of thinking of concepts by their descriptions, in particular by establishing universal properties. Concepts that can be characterized in a universal way receive a certain quality seal, which…
Structured and decorated cospans are broadly applicable frameworks for building bicategories or double categories of open systems. We streamline and generalize these frameworks using central concepts of double category theory. We show that,…
A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for formalizing algorithms that manipulate mathematical expressions. A theory…
Differential categories provide an axiomatization of the basics of differentiation and categorical models of differential linear logic. As differentiation is an important tool throughout quantum mechanics and quantum information, it makes…
In this paper, we explore the 'equivalence principle' (EP): roughly, statements about mathematical objects should be invariant under an appropriate notion of equivalence for the kinds of objects under consideration. In set theoretic…
We introduce the notion of a definable category--a category equivalent to a full subcategory of a locally finitely presentable category that is closed under products, directed colimits and pure subobjects. Definable subcategories are…
I discuss (ontologies_and_ontological_knowledge_bases / formal_methods_and_theories) duality and its category theory extensions as a step toward a solution to Knowledge-Based Systems Theory. In particular I focus on the example of the…
We present the notion of "cyclic double multicategory", as a structure in which to organise multivariable adjunctions and mates. The classic example of a 2-variable adjunction is the hom/tensor/cotensor trio of functors; we generalise this…