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100 1  East, James |c(Professor of mathematics), |eauthor.
245 10 Congruence Lattices of Ideals in Categories and (Partial) Semigroups / |cJames East and Nik Ruskuc.
250    First edition.
264  1 Providence, RI : |bAmerican Mathematical Society, |c[2023]
264  4  |c©2023
300    1 online resource (144 pages)
336    text |btxt |2rdacontent
337    computer |bc |2rdamedia
338    online resource |bcr |2rdacarrier
490 1  Memoirs of the American Mathematical Society Series ; |vVolume 284
505 0  Cover -- Title page -- Acknowledgments -- Chapter 1. Introduction -- Chapter 2. Categories and partial semigroups -- 2.1. Preliminaries -- 2.2. Congruences -- 2.3. Useful lemmas -- Chapter 3. Ideal extensions -- 3.1. Generation and separation properties -- 3.2. Liftable congruences -- 3.3. Congruences on ideal extensions -- Chapter 4. Chains of ideals -- 4.1. Congruences on chains of ideals -- 4.2. Partial rectangular bands -- 4.3. Short retractable chains -- 4.4. Short non-retractable chains -- 4.5. Visualisation conventions -- Chapter 5. Transformation categories -- 5.1. Definitions and preliminaries on \T -- 5.2. Green's relations and multiplicative properties in \T -- 5.3. Congruences on ideals of \T -- 5.4. Planar and annular reducts of \T -- 5.5. Other categories of transformations -- Chapter 6. Partition categories -- 6.1. Definitions and preliminaries on \P -- 6.2. Green's relations and multiplicative properties in \P -- 6.3. Congruences on ideals of \P -- 6.4. Planar and annular reducts of \P -- 6.5. Partial Brauer categories -- Chapter 7. Brauer categories -- 7.1. Definitions and preliminaries on \B -- 7.2. Green's relations and multiplicative properties in \B -- 7.3. Congruences on ideals of \B: the odd case -- 7.4. Congruences on ideals of \B: the even case -- 7.5. Planar and annular reducts of \B -- Chapter 8. Temperley-Lieb and anti-Temperley-Lieb categories -- 8.1. Multiplicative properties in \TL and \TLpm -- 8.2. Congruences on ideals of \TL and \TLpm: the odd case -- 8.3. Congruences on ideals of \TL: the even case -- 8.4. Congruences on ideals of \TLpm: the even case -- Chapter 9. Jones and anti-Jones categories -- 9.1. Multiplicative properties in \JJ and \Jpm -- 9.2. Congruences on ideals of \JJ and \Jpm: the odd case -- 9.3. Congruences on ideals of \JJ and \Jpm: the even case.
505 8  Chapter 10. Categories and partial semigroups with ˝-congruences -- 10.1. ℋ-congruences -- 10.2. More on chains of ideals -- Chapter 11. Linear and projective linear categories -- 11.1. Definitions and preliminaries on \LL and \PL -- 11.2. Green's relations and multiplicative properties in \LL and \PL -- 11.3. Congruences on ideals of \LL -- 11.4. Visualising the lattices -- 11.5. Congruences on ideals of \PL -- Chapter 12. Partial braid categories -- 12.1. Definitions and preliminaries on \IB -- 12.2. Green's relations and multiplicative properties in \IB -- 12.3. Congruences on ideals of \IB -- Bibliography -- Back Cover.
520    "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"-- |cProvided by publisher.
588    Description based on print version record.
504    Includes bibliographical references.
650  0 Congruences (Geometry)
650  0 Categories (Mathematics)
650  0 Semigroups.
700 1  Ruškuc, Nik, |eauthor.
830  0 Memoirs of the American Mathematical Society ; |vVolume 284.
906    BOOK