Related papers: Bicategorical type theory: semantics and syntax
Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…
Many definitions of weak and strict $\infty$-categories have been proposed. In this paper we present a definition for $\infty$-categories with strict associators, but which is otherwise fully weak. Our approach is based on the existing type…
This paper presents a type theory in which it is possible to directly manipulate $n$-dimensional cubes (points, lines, squares, cubes, etc.) based on an interpretation of dependent type theory in a cubical set model. This enables new ways…
Recent work in set theory indicates that there are many different notions of 'set', each captured by a different collection of axioms, as proposed by J. Hamkins in [Ham11]. In this paper we strive to give one class theory that allows for a…
In recent work, we introduced a new semantics for conditionals, covering a large class of what we call preconditionals. In this paper, we undertake an axiomatic study of preconditionals and subclasses of preconditionals. We then prove that…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…
This paper describes a formal proof library, developed using the Coq proof assistant, designed to assist users in writing correct diagrammatic proofs, for 1-categories. This library proposes a deep-embedded, domain-specific formal language,…
Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof rules of regular logic in terms of the free…
Semantic vectors are learned from data to express semantic relationships between elements of information, for the purpose of solving and informing downstream tasks. Other models exist that learn to map and classify supervised data. However,…
Coherence is here demonstrated for sesquicartesian categories, which are categories with nonempty finite products and arbitrary finite sums, including the empty sum, where moreover the first and the second projection from the product of the…
Let $\mathscr{C}$ be an extriangulated category with enough projectives and injectives. We give a new definition of tilting subcategories of $\mathscr{C}$ and prove it coincides with the definition given in [19]. As applications, we…
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…
We establish and advocate for a novel branch of category theory, centered around strong dinatural transformations (herein known as "paranatural transformations"). Paranatural transformations generalize natural transformations to…
In this expository paper we explain in detail how to construct bicategorical colimits of several kinds of tensor categories, for example essentially small finitely cocomplete K-linear tensor categories. The constructions are direct and…
A major difficulty in developing and maintaining very large knowledge bases originates from the variety of forms in which knowledge is made available to the KB builder. The objective of this research is to bring together two complementary…
This paper proposes a way to compute the meanings associated with sentences with generic noun phrases corresponding to the generalized quantifier most. We call these generics specimens and they resemble stereotypes or prototypes in lexical…
We want to replace categories, functors and natural transformations by categories, open functors and open natural transformations. In analogy with open dynamical systems, the adjective open is added here to mean that some external…
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,…
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 examine the class of languages that can be defined entirely in terms of provability in an extension of the sorted type theory (Ty_n) by embedding the logic of phonologies, without introduction of special types for syntactic entities.…