Categorical constructions in C*-algebra theory

Categorical Code Constructions

We study categories of codes and precodes. The objects in these categories capture the encoding and decoding process of error control codes, source codes, or cryptographic codes. We show that these categories are complete and cocomplete. This gives a wealth of new code constructions.

Categorical Algebra

1. Introduction. Category, functor, and natural transformation of functors are notions of great generality—and consequent simplicity. They apply to many different parts of mathematics. Now 22 years old, they have recently attracted especially active interest in many quarters. This interest is probably a reflection of the very rapid current proliferation of mathematical ideas—a situation favorin...

A History of Selected Topics in Categorical Algebra I: From Galois Theory to Abstract Commutators and Internal Groupoids

This paper is a chronological survey, with no proofs, of a direction in categorical algebra, which is based on categorical Galois theory and involves generalized central extensions, commutators, and internal groupoids in Barr exact Mal’tsev and more general categories. Galois theory proposes a notion of central extension, and motivates the study of internal groupoids, which is then used as an a...

R – Conformal Symmetries in 2 D Nonlocal Quantum Field Theory , Categorical Representation Theory , and Virasoro Algebra

a history of selected topics in categorical algebra i: from galois theory to abstract commutators and internal groupoids

this paper is a chronological survey, with no proofs, of a direction in categorical algebra, which is based on categorical galois theory and involves generalized central extensions, commutators, and internal groupoids in barr exact mal’tsev and more general categories. galois theory proposes a notion of central extension, and motivates the study of internal groupoids, which is then used as an a...