Related papers: Linear Arboreal Categories
Taking a Feynman categorical perspective, several key aspects of the geometry of surfaces are deduced from combinatorial constructions with graphs. This provides a direct route from combinatorics of graphs to string topology operations via…
String languages recognizable in (deterministic) log-space are characterized either by two-way (deterministic) multi-head automata, or following Immerman, by first-order logic with (deterministic) transitive closure. Here we elaborate this…
Session types provide guarantees about concurrent behaviour and can be understood through their correspondence with linear logic, with propositions as sessions and proofs as processes. However, a strictly linear setting is somewhat…
Proto-exact and parabelian categories serve as non-additive analogues of exact and quasi-abelian categories, respectively. They give rise to algebraic K-theory and Hall algebras similarly to the additive setting. We show that every…
The Alexandrov topology affords a well-known semantics of modal necessity and possibility. This paper develops an Alexandrov topological semantics of intuitionistic propositional modal logic internally in any elementary topos. This is done…
Labeled infinite trees provide combinatorial interpretations for many integer sequences generated by nested recurrence relations. Typically, such sequences are monotone increasing. Several of these sequences also have straightforward…
We give a precise description of combed trees in terms of Kelly-Mac Lane graphs. We show that any combed tree is uniquely expressed as an allowable Kelly-Mac Lane graph of a certain shape. Conversely, we show that any such Kelly-Mac Lane…
Arboreal networks are a generalization of rooted trees, defined by keeping the tree-like structure, but dropping the requirement for a single root. Just as the class of cographs is precisely the class of undirected graphs that can be…
These notes provide a description of the abelian categories that arise as categories of coherent sheaves on weighted projective lines. Two different approaches are presented: one is based on a list of axioms and the other yields a…
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…
Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…
The growing complexity of modern practical problems puts high demands on the mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice becomes…
Differential linear categories provide the categorical semantics of the multiplicative and exponential fragments of Differential Linear Logic. Briefly, a differential linear category is a symmetric monoidal category that is enriched over…
In this paper, we introduce the notion of parabolic log convergent isocrystals on smooth varieties endowed with a simple normal crossing divisor, which is a kind of $p$-adic analogue of the notion of parabolic bundles on smooth varieties…
We seize the opportunity of the publication of selected papers from the \emph{Logic, categories, semantics} workshop in the \emph{Journal of Applied Logic} to survey some current trends in logic, namely intuitionistic and linear type…
We propose a method that learns a discriminative yet semantic space for object categorization, where we also embed auxiliary semantic entities such as supercategories and attributes. Contrary to prior work which only utilized them as side…
A number of domain specific languages, such as circuits or data-science workflows, are best expressed as diagrams of boxes connected by wires. Unfortunately, functional languages have traditionally been ill-equipped to embed this sort of…
We provide a unified operational framework for the study of causality, non-locality and contextuality, in a fully device-independent and theory-independent setting. Our work has its roots in the sheaf-theoretic framework for contextuality…
This paper presents a batch classifier that has been improved from the earlier version and fixed a mistake in the earlier paper. Two important changes have been made. Each category is represented by a classifier, where each classifier…
We define two general classes of nonabelian sandpile models on directed trees (or arborescences) as models of nonequilibrium statistical phenomena. These models have the property that sand grains can enter only through specified reservoirs,…