Details

Subject(s)

• Congruences (Geometry) [Browse]
• Categories (Mathematics) [Browse]
• Semigroups [Browse]

Author

• Ruškuc, Nik [Browse]

Series

Memoirs of the American Mathematical Society ; 1408. [More in this series]

Summary note

"This monograph presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative process of stacking certain normal subgroup lattices on top of each other to successively build congruence lattices of a chain of ideals. This is applied to several specific categories of: transformations; order/orientation preserving/reversing transformations; partitions; planar/annular partitions; Brauer, Temperley-Lieb and Jones partitions; linear and projective linear transformations; and partial braids. Special considerations are needed for certain small ideals, and technically more intricate theoretical underpinnings for the linear and partial braid categories"-- Provided by publisher.

Bibliographic references

Includes bibliographical references.

Contents

• Categories and partial semigroups
• Ideal extensions
• Chains of ideals
• Transformation categories
• Partition categories
• Brauer categories
• Temperley-Lieb and anti-Temperley-Lieb categories
• Jones and anti-Jones categories
• Categories and partial semigroups with H -congruences
• Linear and projective linear categories
• Partial braid categories.

Show 8 more Contents items

ISBN

• 9781470462697 ((paperback))
• 1470462699

LCCN

2023014514

OCLC

1378080524

Statement on language in description

Princeton University Library aims to describe library materials in a manner that is respectful to the individuals and communities who create, use, and are represented in the collections we manage. Read more...