Related papers: Introduction to Categories and Categorical Logic
The aim of these lectures is to give a short introduction to forcing. We will avoid metamathematical issues as much as possible and similarly we will avoid performing the actual construction of forcing. We assume familiarity with basic…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
The primary theme of this investigation is a decision theoretic account of conditional ought statements (e.g., "You ought to do A, if C") that rectifies glaring deficiencies in classical deontic logic. The resulting account forms a sound…
A non-self-contained gathering of notes on category theory, including the definition of locally cartesian closed category, of the cartesian structure in slice categories, or of the pseudo-cartesian structure on Eilenberg-Moore categories.…
This brief brochure is intended to present a philosophical theory known as relational materialism. We introduce the postulates and principles of the theory, articulating its ontological and epistemological content using the language of…
This book is an introduction to 2-categories and bicategories, assuming only the most elementary aspects of category theory. A review of basic category theory is followed by a systematic discussion of 2-/bicategories, pasting diagrams, lax…
We introduce a new approach to the study of operational theories of physics using category theory. We define a generalisation of the (causal) operational-probabilistic theories of Chiribella et al. and establish their correspondence with…
These lecture notes concern the basics of the theory of process behaviour. First the concept of a (labelled) transition system receives ample treatment and then the following issues concerning process behaviour are elaborated in the setting…
In context of efforts of composing category-theoretic and logical methods in the area of knowledge representation we propose the notion of conceptory. We consider intersection/union and other constructions in conceptories as expressive…
The major concern in the study of categories of logics is to describe condition for preservation, under the a method of combination of logics, of meta-logical properties. Our complementary approach to this field is study the "global"…
Modeling a sequence of design steps, or a sequence of parameter settings, yields a sequence of dynamical systems. In many cases, such a sequence is intended to approximate a certain limit case. However, formally defining that limit turns…
Invited contribution to the Encyclopedia of Mathematical Physics. We give an introduction to the homotopical theory of higher categories, focused on motivating the definitions of the basic objects, namely $\infty$-categories and…
Various concerns suggest looking for internal co-categories in categories with strong logical structure. It turns out that in any coherent category, all co-categories are co-equivalence relations.
We consider categorical logic on the category of Hilbert spaces. More generally, in fact, any pre-Hilbert category suffices. We characterise closed subobjects, and prove that they form orthomodular lattices. This shows that quantum logic is…
We present a new, category theoretic point of view on finite Ramsey theory. Our aims are as follows: -- to define the category theoretic notions needed for the development of finite Ramsey Theory, -- to state, in terms of these notions, the…
Regular logic is the fragment of first order logic generated by $=$, $\top$, $\wedge$, and $\exists$. A key feature of this logic is that it is the minimal fragment required to express composition of binary relations; another is that it is…
This paper provides a self-contained first introduction to description logics (DLs). The main concepts and features are explained with examples before syntax and semantics of the DL SROIQ are defined in detail. Additional sections review…
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…
Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, alpha-equivalence). This article investigates…
There are many books designed to introduce category theory to either a mathematical audience or a computer science audience. In this book, our audience is the broader scientific community. We attempt to show that category theory can be…