Related papers: Doctrines, modalities and comonads
We construct a 2-equivalence $\mathfrak{CohTheory}^\text{op} \simeq \mathfrak{TypeSpaceFunc}$. Here $\mathfrak{CohTheory}$ is the 2-category of positive theories and $\mathfrak{TypeSpaceFunc}$ is the 2-category of type space functors. We…
Notions of guardedness serve to delineate the admissibility of cycles, e.g. in recursion, corecursion, iteration, or tracing. We introduce an abstract notion of guardedness structure on a symmetric monoidal category, along with a…
Syntactic theory has traditionally adopted a constructivist approach, in which a set of atomic elements are manipulated by combinatory operations to yield derived, complex elements. Syntactic structure is thus seen as the result or discrete…
A transduction provides us with a way of using the monadic second-order language of a structure to make statements about a derived structure. Any transduction induces a relation on the set of these structures. This article presents a…
Abstract inner automorphisms can be used to promote any category into a 2-category, and we study two-dimensional limits and colimits in the resulting 2-categories. Existing connected colimits and limits in the starting category become…
In the theory of operads we consider functors of generalized symmetric powers defined by sums of coinvariant modules under actions of symmetric groups. One observes classically that the construction of symmetric functors provides an…
The concept of a clone is central to many branches of mathematics, such as universal algebra, algebraic logic, and lambda calculus. Abstractly a clone is a category with two objects such that one is a countably infinite power of the other.…
We present an empirical study aimed at analysing the use of viewpoints in an industrial Concurrent Engineering context. Our focus is on the viewpoints expressed in the argumentative process taking place in evaluation meetings. Our results…
We give a description of unital operads in a symmetric monoidal category as monoids in a monoidal category of unital $\Lambda$-sequences. This is a new variant of Kelly's old description of operads as monoids in the monoidal category of…
Mathematical programs with disjunctive constraints (MPDCs for short) cover several different problem classes from nonlinear optimization including complementarity-, vanishing-, cardinality-, and switching-constrained optimization problems.…
INTRODUCTION This papers deals with partial differential equations of second order, linear, with constant and not constant coefficients, in two variables, which admit real characteristics. I face the study of PDEs with the mentality of the…
Ordered item response models that are in common use can be divided into three groups, cumulative, sequential and adjacent categories model. The derivation and motivation of the models is typically based on the assumed presence of latent…
This paper studies the homotopy theory of the Grothendieck construction using model categories and semi-model categories, provides a unifying framework for the homotopy theory of operads and their algebras and modules, and uses this…
Combinatorial games are widely used in finite model theory, constraint satisfaction, modal logic and concurrency theory to characterize logical equivalences between structures. In particular, Ehrenfeucht-Fraisse games, pebble games, and…
Proofs of coherence in category theory, starting from Mac Lane's original proof of coherence for monoidal categories, are sometimes based on confluence techniques analogous to what one finds in the lambda calculus, or in term-rewriting…
Identifying and explaining the structure of complex networks at different scales has become an important problem across disciplines. At the mesoscale, modular architecture has attracted most of the attention. At the macroscale, other…
(Pre)closure spaces are a generalization of topological spaces covering also the notion of neighbourhood in discrete structures, widely used to model and reason about spatial aspects of distributed systems. In this paper we introduce an…
Programming with logic for sophisticated applications must deal with recursion and negation, which together have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a…
Monadic second order logic is the expansion of first order logic by quantifiers ranging over unary relations. We study the shared monadic second order theory of finite linear orders, i.e. the pseudofinite monadic second order theory of…
Abbott, Altenkirch, Ghani and others have taught us that many parameterized datatypes (set functors) can be usefully analyzed via container representations in terms of a set of shapes and a set of positions in each shape. This paper builds…