Related papers: About Opposition and Duality in Paraconsistent Typ…
In this short note, we construct a class of models of an extension of homotopy type theory, which we call homotopy type theory with an interval type.
We start in this work the study of the relation between the theory of regularity structures and paracontrolled calculus. We give a paracontrolled representation of the reconstruction operator and provide a natural parametrization of the…
A continuous cohomology theory for topological quandles is introduced, and compared to the algebraic theories. Extensions of topological quandles are studied with respect to continuous 2-cocycles, and used to show the differences in second…
We interpret the additive middle convolution operation in terms of the Harnad duality, and as an application, generalize the operation to have a multi-parameter and act on irregular singular systems.
In this article, we study translations between variants of defaults logics such that the extensions of the theories that are the input and the output of the translation are in a bijective correspondence. We assume that a translation can…
This paper assesses when the validity of difference-in-differences depends on functional form. We provide a novel characterization: the parallel trends assumption holds under all strictly monotonic transformations of the outcome if and only…
The cartesian structure possessed by relations, spans, profunctors, and other such morphisms is elegantly expressed by universal properties in double categories. Though cartesian double categories were inspired in part by the older program…
In this addendum to [4], we provide a pair of counterexamples relevant to the theory of implicit operations. More precisely, we exhibit a pp expansion of a variety that fails to be a variety (although it is a quasivariety). Furthermore, we…
We study the conservativity of extensions by additional strict equalities of dependent type theories (and more general second-order generalized algebraic theories). The conservativity of Extensional Type Theory over Intensional Type Theory…
In the theory of programming languages, type inference is the process of inferring the type of an expression automatically, often making use of information from the context in which the expression appears. Such mechanisms turn out to be…
The goal of this paper is to introduce the notion of polyconvolution for Fourier-cosine, Laplace integral operators, and its applications. The structure of this polyconvolution operator and associated integral transforms are investigated in…
The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.
Path polymorphism is the ability to define functions that can operate uniformly over arbitrary recursively specified data structures. Its essence is captured by patterns of the form $x\,y$ which decompose a compound data structure into its…
The natural duality between "topological" and "regular," both considered as convergence space properties, extends naturally to p-regular convergence spaces, resulting in the new concept of a p-topological convergence space. Taking advantage…
We introduce so-called cone topologies of paratopological groups, which are a wide way to construct counterexamples, especially of examples of compact-like paratopological groups with discontinuous inversion. We found a simple interplay…
We study dualities between classes of relational topological structures, given by Hom-functors. We show that there exists a 2-element structure with infinitely many relations, which reconstructs all other structures generated by a 2-element…
We provide a treatment of isomorphism within a set-theoretic formulation of dependent type theory. Type expressions are assigned their natural set-theoretic compositional meaning. Types are divided into small and large types --- sets and…
We present the type system $\mathtt{d}$, an extended type system with lambda-typed lambda-expressions. It is related to type systems originating from the Automath project. $\mathtt{d}$ extends existing lambda-typed systems by an existential…
In [1], systems of weakening of intuitionistic negation logic called Z_n and CZ_n were developed in the spirit of da Costa's approach(c.f. [2]) by preserving, differently from da Costa, its fundamental properties: antitonicity, inversion…
Starting from the concept of involution of field equations, a universal method is proposed for constructing consistent interactions between the fields. The method equally well applies to the Lagrangian and non-Lagrangian equations and it is…