• Corpus ID: 252212278

Constructing linear bicategories

@inproceedings{Blute2022ConstructingLB,
  title={Constructing linear bicategories},
  author={Richard Blute and Rose Kudzman-Blais and Susan B. Niefield},
  year={2022}
}
Linearly distributive categories were introduced to model the tensor/par fragment of linear logic, without resorting to the use of negation. Linear bicategories are the bicategorical version of linearly distributive categories. Essentially, a linear bicategory has two forms of composition, each determining the structure of a bicategory, and the two compositions are related by a linear distribution. After the initial paper on the subject, there was little further work as there seemed to be a… 

References

SHOWING 1-10 OF 27 REFERENCES

Introduction to linear bicategories

Linear bicategories are a generalization of bicategories in which the one horizontal composition is replaced by two (linked) horizontal compositions. These compositions provide a semantic model for

Weakly distributive categories

Quantales and (noncommutative) linear logic

  • D. Yetter
  • Philosophy
    Journal of Symbolic Logic
  • 1990
It is the purpose of this paper to make explicit the connection between J.-Y. Girard's “linear logic” [4], and certain models for the logic of quantum mechanics, namely Mulvey's “quantales” [9]. This

Pointwise extensions and sketches in bicategories

We make a few remarks concerning pointwise extensions in a bicategory which include the case of bicategories of enriched categories. We show that extensions, pointwise or not, can be replaced by

Constructing locales from quantales

We recall that a locale is a complete lattice L satisfying a ∧ (∨bα) = ∨(a ∧ bα), for all a ∈ L, and {bα} ⊆ L. Examples of locales include the lattices (X) of open subsets of topological spaces X.

Handbook of Weighted Automata

This book covers all the main aspects of weighted automata and formal power series methods, ranging from theory to applications, and presents a detailed survey of the state of the art and pointers to future research.

Linear logic

This column presents an intuitive overview of linear logic, some recent theoretical results, and summarizes several applications oflinear logic to computer science.

Semirings and Affine Equations over Them: Theory and Applications

Preface. Introduction. 1: Semirings. 2: Partially-Ordered Semirings. 3: Complete Semirings. 4: Residuated Semirings. 5: Matrix Semirings. 6: Symmetric Extension of a Semiring. 7: Semimodules. 8:

A 2-Categories Companion

This paper is a rather informal guide to some of the basic theory of 2-categories and bicategories, including notions of limit and colimit, 2-dimensional universal algebra, formal category theory,