Related papers: Elementwise semantics in categories with pull-back…
This paper investigates quantum logic from the perspective of categorical logic, and starts from minimal assumptions, namely the existence of involutions/daggers and kernels. The resulting structures turn out to (1) encompass many examples…
One can imagine a number of mechanisms that could be the cause of brighter/fainter segments of jets. In a sense, jets might be easier to understand if they were featureless. However we observe a wide variety of structures which we call…
Variations on the notions of Reedy model structures and projective model structures on categories of diagrams in a model category are introduced. These allow one to choose only a subset of the entries when defining weak equivalences, or to…
We consider virtual pullbacks in $K$-theory, and show that they are bivariant classes and satisfy certain functoriality. As applications to $K$-theoretic counting invariants, we include proofs of a virtual localization formula for schemes…
Like any other logical theory, domain descriptions in reasoning about actions may evolve, and thus need revision methods to adequately accommodate new information about the behavior of actions. The present work is about changing action…
We establish a theory of complexes of relative correspondences. The theory generalizes the known theory of complexes of correspondences of smooth projective varieties. It will be applied in the sequel of this paper to the construction of…
We define a motive whose realizations afford modular forms (of arbitrary weight) on an indefinite division quaternion algebra. This generalizes work of Iovita--Spiess to odd weights in the spirit of Jordan--Livn\'e. It also generalizes a…
This paper seeks to apply categorical logic to the design of artificial intelligent agents that reason symbolically about objects more richly structured than sets. Using Johnstone's sequent calculus of terms- and formulae-in-context, we…
We propose a categorical framework to reason about scientific explanations: descriptions of a phenomenon meant to translate it into simpler terms, or into a context that has been already understood. Our motivating examples come from systems…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
This note is concerned with the problem of motion modeling in Physics. We aim to use the Time-Variant Local Autocorrelation Polynomial to understand the mathematical model of motion description. The mathematical explanation of the existence…
In [Hitzler and Wendt 2002, 2005], a new methodology has been proposed which allows to derive uniform characterizations of different declarative semantics for logic programs with negation. One result from this work is that the well-founded…
Formal semantics and distributional semantics are distinct approaches to linguistic meaning: the former models meaning as reference via model-theoretic structures; the latter represents meaning as vectors in high-dimensional spaces shaped…
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…
Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…
This article is an introduction to the basic generalized category theory used in recent work on an extension of the theory of categories and categorical logic, including parts of topos theory. We discuss functors, equivalences, natural…
We give interpretations of some known key agreement protocols in the framework of category theory and in this way we give a method of constructing of many new key agreement protocols.
It is well-known that biological phenomena are emergent. Emergent phenomena are quite interesting and amazing. However, they are difficult to be understood. Due to this difficulty, we propose a theory to describe emergence based on a…
This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams. It is hoped that this will be useful not just to mathematicians, but also to physicists, computer scientists, and…
In this paper, we give an overview of some recent work on applying tools from category theory in finite model theory, descriptive complexity, constraint satisfaction, and combinatorics. The motivations for this work come from Computer…