MARC details
| 000 -LEADER |
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| fixed length control field |
03089cam a2200277 i 4500 |
| 001 - CONTROL NUMBER |
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136738 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
ISI Library, Kolkata |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20160407154513.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
141218s2015 riua b 001 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781470421977 (hardback: alk. paper) |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
ISI Library |
| Language of cataloging |
eng |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
510MS |
| Edition number |
23 |
| Item number |
Am512 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Yau, Donald. |
| 245 10 - TITLE STATEMENT |
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| Title |
Foundation for PROPs, algebras, and modules / |
| Statement of responsibility, etc |
Donald Yau and Mark W. Johnson. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
Providence : |
| Name of publisher, distributor, etc |
American Mathematical Society, |
| Date of publication, distribution, etc |
2015. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
xxxi, 311 p. : |
| Other physical details |
illustrations ; |
| Dimensions |
26 cm. |
| 490 0# - SERIES STATEMENT |
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| Series statement |
Mathematical surveys and monographs ; |
| Volume number/sequential designation |
v 203. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Part 1. Wheeled graphs and pasting schemes. <br/>1. Wheeled graphs --<br/>2. Special sets of graphs --<br/>3. Basic operations on wheeled graphs --<br/>4. Graph groupoids --<br/>5. Graph substitution --<br/>6. Properties of graph substitution --<br/>7. Generators of graphs --<br/>8. Pasting schemes --<br/>9. Well-matched pasting schemes --<br/><br/>Part 2. Generalized PROPs, algebras, and modules. <br/>10. Generalized PROPs --<br/>11. Biased characterizations of generalized PROPs --<br/>12. Functors of generalized PROPs --<br/>13. Algebra over generalized PROPs --<br/>14. Alternative descriptions of generalized PROPs --<br/>15. Modules over generalized PROPs --<br/>16. May modules over algebras over operads --<br/>Bibliography --<br/>Index. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
PROPs and their variants are extremely general and powerful machines that encode operations with multiple inputs and multiple outputs. In this respect PROPs can be viewed as generalizations of operads that would allow only a single output. Variants of PROPs are important in several mathematical fields, including string topology, topological conformal field theory, homotopical algebra, deformation theory, Poisson geometry, and graph cohomology. The purpose of this monograph is to develop, in full technical detail, a unifying object called a generalized PROP. Then with an appropriate choice of pasting scheme, one recovers (colored versions of) dioperads, half-PROPs, (wheeled) operads, (wheeled) properads, and (wheeled) PROPs. Here the fundamental operation of graph substitution is studied in complete detail for the first time, including all exceptional edges and loops as examples of a new definition of wheeled graphs. A notion of generators and relations is proposed which allows one to build all of the graphs in a given pasting scheme from a small set of basic graphs using graph substitution. This provides information at the level of generalized PROPs, but also at the levels of algebras and of modules over them. Working in the general context of a symmetric monoidal category, the theory applies for both topological spaces and chain complexes in characteristic zero. This book is useful for all mathematicians and mathematical physicists who want to learn this new powerful technique. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Permutation groups. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Categories (Mathematics) |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Modules (Algebra) |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Johnson, Mark W., |
| Relator term |
author |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
Books |
