# 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

- MathematicsMathematical Structures in Computer Science
- 2000

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…

### Quantales and (noncommutative) linear logic

- PhilosophyJournal 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

- Mathematics
- 2014

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

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1988

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

- Computer Science
- 2009

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

- Computer Science, PhilosophySIGA
- 1992

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

- Mathematics
- 2003

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

- Mathematics, Philosophy
- 2010

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,…