Related papers: Two-dimensional transducers

We present the notion of "cyclic double multicategory", as a structure in which to organise multivariable adjunctions and mates. The classic example of a 2-variable adjunction is the hom/tensor/cotensor trio of functors; we generalise this…

This is the first of a pair of papers where we construct and investigate a closed monoidal structure on the category of generalized algebraic theories (in the sense of Cartmell). In the present text, as a starting point, we define the…

Fixpoint operators are tools to reason on recursive programs and data types obtained by induction (e.g. lists, trees) or coinduction (e.g. streams). They were given a categorical treatment with the notion of categories with fixpoints. A…

In this paper we investigate the construction of bicategories of fractions originally described by D. Pronk: given any bicategory $\mathcal{C}$ together with a suitable class of morphisms $\mathbf{W}$, one can construct a bicategory…

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…

A Hilbert bimodule is a right Hilbert module X over a C*-algebra A together with a left action of A as adjointable operators on X. We consider families X = {X_s :s\in P} of Hilbert bimodules, indexed by a semigroup P, which are endowed with…

Structures where we have both a contravariant (pullback) and a covariant (pushforward) functoriality that satisfy base change can be encoded by functors out of ($\infty$-)categories of spans (or correspondences). In this paper we study the…

This thesis focuses on topics in 2-category theory: in particular on double categories, pseudomonads and codescent objects. In Chapter 2 we recall all the necessary notions. In Chapter 3 we show that factorization systems can be…

To formalize calculations in linear algebra for the development of efficient algorithms and a framework suitable for functional programming languages and faster parallelized computations, we adopt an approach that treats elements of linear…

We denote the monoidal bicategory of two-sided modules (also called profunctors, bimodules and distributors) between categories by $\mathrm{Mod}$; the tensor product is cartesian product of categories. For a groupoid $\scr{G}$, we study the…

We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is…

For a finite dimensional algebra $A$, we prove that the bounded homotopy category of projective $A$-modules and the bounded derived category of $A$-modules are dual to each other via certain categories of locally-finite cohomological…

Several abstract machines that operate on symbolic input alphabets have been proposed in the last decade, for example, symbolic automata or lattice automata. Applications of these types of automata include software security analysis and…

In this thesis I lift the Curry--Howard--Lambek correspondence between the simply-typed lambda calculus and cartesian closed categories to the bicategorical setting, then use the resulting type theory to prove a coherence result for…

We show that 2-categories of the form $\mathscr{B}\mbox{-}\mathbf{Cat}$ are closed under slicing, provided that we allow $\mathscr{B}$ to range over bicategories (rather than, say, monoidal categories). That is, for any…

The aim of this article is to study certain categorical-algebraic frameworks for basic homological algebra, introduced in arXiv:2404.15896, with the aim of better understanding the differences between them. We focus on homological…

Definable subcategories may be extended along a ring homomorphism directly, by using their defining conditions in the new module category, or by tensoring up with the new ring. We investigate what is preserved and reflected by these…

We propose a generalisation of Exel's crossed product by a single endomorphism and a transfer operator to the case of actions of abelian semigroups of endomorphisms and associated transfer operators. The motivating example for our…

Unitary Ribbon Fusion Categories (URFC) formalize anyonic theories. It has been widely assumed that the same category formalizes a topological quantum computing model. However, in previous work, we addressed and resolved this confusion and…

We introduce pseudoalgebras for relative pseudomonads and develop their theory. For each relative pseudomonad $T$, we construct a free--forgetful relative pseudoadjunction that exhibits the bicategory of $T$-pseudoalgebras as terminal among…