Related papers: Classical Distributive Restriction Categories
The classical causal relations between a set of variables, some observed and some latent, can induce both equality constraints (typically conditional independences) as well as inequality constraints (Instrumental and Bell inequalities being…
Differential categories axiomatize the basics of differentiation and provide categorical models of differential linear logic. A differential category is said to have antiderivatives if a natural transformation $\mathsf{K}$, which all…
Computational effects may often be interpreted in the Kleisli category of a monad or in the coKleisli category of a comonad. The duality between monads and comonads corresponds, in general, to a symmetry between construction and…
Restriction categories were introduced as a way of generalising the notion of partial map categories. In this paper, we define cocomplete restriction category, and give the free cocompletion of a small restriction category as a suitably…
It is proved that equalities between arrows assumed for cartesian categories are maximal in the sense that extending them with any new equality in the language of free cartesian categories collapses a cartesian category into a preorder. An…
A significant part of quantum theory can be obtained from a single innovation relative to classical theories, namely, that there is a fundamental restriction on the sorts of statistical distributions over physical states that can be…
We exhibit an adjunction between a category of abstract algebras of partial functions that we call difference-restriction algebras and a category of Hausdorff \'etale spaces. Difference-restriction algebras are those algebras isomorphic to…
In flowchart languages, predicates play an interesting double role. In the textual representation, they are often presented as conditions, i.e., expressions which are easily combined with other conditions (often via Boolean combinators) to…
Restriction categories were introduced to provide an axiomatic setting for the study of partially defined mappings; they are categories equipped with an operation called restriction which assigns to every morphism an endomorphism of its…
We ascertain conditions and structures on categories and semigroups which admit the construction of pseudo-products and trace products respectively, making their connection as precise as possible. This topic is modelled on the ESN Theorem…
Unlike quantum correlations, the shareability of classical correlations (CCs) between two-parties of a multipartite state is assumed to be free since there exist states for which CCs for each of the reduced states can simultaneously reach…
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This…
Classical finite association schemes lead to a finite-dimensional algebras which are generated by finitely many stochastic matrices. Moreover, there exist associated finite hypergroups. The notion of classical discrete association schemes…
The study of categories abstracting the structural properties of relations has been extensively developed over the years, resulting in a rich and diverse body of work. A previous paper offered a survey providing a modern and comprehensive…
Restriction categories provide a categorical framework for partiality. In this paper, we introduce three new categorical theories for partiality: local categories, partial categories, and inclusion categories. The objects of a local…
We study a categorical condition on relations, which is a categorical formulation of J\'onsson's characterisation of congruence distributive varieties. Categories satisfying these conditions need not be varieties; for instance, the dual of…
We demonstrate the effectiveness of the categorical distribution as a neural network output for next event prediction. This is done for both discrete-time and continuous-time event sequences. To model continuous-time processes, the…
During the last decades, a lot of effort was put into identifying decidable fragments of first-order logic. Such efforts gave birth, among the others, to the two-variable fragment and the guarded fragment, depending on the type of…
In recent work, symmetric dagger-monoidal (SDM) categories have emerged as a convenient categorical formalization of quantum mechanics. The objects represent physical systems, the morphisms physical operations, whereas the tensors describe…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…