Related papers: Rewriting Modulo Traced Comonoid Structure
We argue that the quantum-theoretical structures studied in several recent lines of research cannot be adequately described within the standard framework of quantum circuits. This is in particular the case whenever the combination of…
A variant of the trace in a monoidal category is given in the setting of closed monoidal derivators, which is applicable to endomorphisms of fiberwise dualizable objects. Functoriality of this trace is established. As an application, an…
We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this…
Sesqui-pushout (SqPO) rewriting is a variant of transformations of graph-like and other types of structures that fit into the framework of adhesive categories where deletion in unknown context may be implemented. We provide the first…
In our paper "On D-module of categories I", we provide two different methods of constructing D-module structures on the complex computing periodic cyclic homology associated to a family of stable infinity categories. One is based on a…
In reinforcement learning, conducting task composition by forming cohesive, executable sequences from multiple tasks remains challenging. However, the ability to (de)compose tasks is a linchpin in developing robotic systems capable of…
This paper is a fundamental study of comodules and contramodules over a comonoid in a symmetric closed monoidal category. We study both algebraic and homotopical aspects of them. Algebraically, we enrich the comodule and contramodule…
The syntactic categories of categorial grammar formalisms are structured units made of smaller, indivisible primitives, bound together by the underlying grammar's category formation rules. In the trending approach of constructive…
Techniques from higher categories and higher-dimensional rewriting are becoming increasingly important for understanding the finer, computational properties of higher algebraic theories that arise, among other fields, in quantum…
Topology diagrams are widely seen in power system applications, but their automatic generation is often easier said than done. When facing power transmission systems with strongly-meshed structures, existing approaches can hardly produce…
Formally verifying the properties of formal systems using a proof assistant requires justifying numerous minor lemmas about capture-avoiding substitution. Despite work on category-theoretic accounts of syntax and variable binding, raw,…
Dominant sequence models like the Transformer represent structure implicitly through dense attention weights, incurring quadratic complexity. We propose RewriteNets, a novel neural architecture built on an alternative paradigm: explicit,…
Trace slicing is a widely used technique for execution trace analysis that is effectively used in program debugging, analysis and comprehension. In this paper, we present a backward trace slicing technique that can be used for the analysis…
Motivated by the recent interest in models of guarded (co-)recursion, we study their equational properties. We formulate axioms for guarded fixpoint operators generalizing the axioms of iteration theories of Bloom and \'Esik. Models of…
We construct a thin double category HS (Hub-and-Spoke) whose objects are closed subsets of standard simplices, horizontal morphisms are continuous maps representing portfolio re-implementation processes, and vertical morphisms are closed…
Hasegawa showed that control flow in programming languages -- while loops and if-then-else statements -- can be modeled using traced cocartesian categories, such as the category $\mathbf{Set}_*$ of pointed sets. In this paper we define an…
Parallel tensor network contraction algorithms have emerged as the pivotal benchmarks for assessing the classical limits of computation, exemplified by Google's demonstration of quantum supremacy through random circuit sampling. However,…
Deduction systems and graph rewriting systems are compared within a common categorical framework. This leads to an improved deduction method in diagrammatic logics.
We present a term rewriting system that models the dynamic aspects of the free cornering with protocol choice of a monoidal category, which has been proposed as a categorical model of process interaction. This term rewriting system is…
Thomason's Homotopy Colimit Theorem has been extended to bicategories and this extension can be adapted, through the delooping principle, to a corresponding theorem for diagrams of monoidal categories. In this version, we show that the…