Congruence Lattices of Ideals in Categories and (Partial) Semigroups

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...

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Bibliographic Details
Main Authors: East, James, Ruškuc, Nik
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2023
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Categories (Mathematics)
Congruences (Geometry)
Semigroups
Brauer categories
chains of ideals
ideals
Categories
<inline-formula content-type="math/mathml"> H \mathscr {H} </inline-formula>-congruences
semigroups
projective linear categories
partial braid categories
transformation categories
Jones categories
linear categories
partition categories
diagram categories
congruences
lattices
Temperley-Lieb categories
ISBN:9781470462697, 1470462699
ISSN:0065-9266, 1947-6221
Online Access:Get full text
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Summary: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.
Bibliography:Includes bibliographical references (p. 125-129)
April 2023, volume 284, number 1408 (fourth of 6 numbers)
ISBN:9781470462697
1470462699
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1408