Higher Operads Higher Categories London Mathematical Society Lecture Note Series 1st Edition by Tom Leinster ISBN 0521532159 978-0521532150
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Product details:
ISBN 10: 0521532159
ISBN 13: 978-0521532150
Author: Tom Leinster
Category theory has experienced a resurgence in popularity recently because of new links with topology and mathematical physics. This book provides a clearly written account of higher order category theory and presents operads and multicategories as a natural language for its study. Tom Leinster has included necessary background material and applications as well as appendices containing some of the more technical proofs that might have disrupted the flow of the text.
Table of contents:
Part I. Background
1 Classical categorical structures
1.1 Categories
1.2 Monoidal categories
1.3 Enrichment
1.4 Strict n-categories
1.5 Bicategories
2 Classical operads and multicategories
2.1 Classical multicategories
2.2 Classical operads
2.3 Further theory
3 Notions of monoidal category
3.1 Unbiased monoidal categories
3.2 Algebraic notions of monoidal category
3.3 Non-algebraic notions of monoidal category
3.4 Notions of bicategory
Part II. Operads
4 Generalized operads and multicategories: basics
4.1 Cartesian monads
4.2 Operads and multicategories
4.3 Algebras
5 Example: fc-multicategories
5.1 fc-multicategories
5.2 Weak double categories
5.3 Monads, monoids and modules
6 Generalized operads and multicategories: further theory
6.1 More on monads
6.2 Multicategories via monads
6.3 Algebras via fibrations
6.4 Algebras via endomorphisms
6.5 Free multicategories
6.6 Structured categories
6.7 Change of shape
6.8 Enrichment
7 Opetopes
7.1 Opetopes
7.2 Categories of pasting diagrams
7.3 A category of trees
7.4 Opetopic sets
7.5 Weak n-categories: a sketch
7.6 Many in, many out
Part III. n-categories
8 Globular operads
8.1 The free strict ω-category monad
8.2 Globular operads
8.3 Algebras for globular operads
9 A definition of weak n-category
9.1 Contractions
9.2 Weak ω-categories
9.3 Weak n-categories
9.4 Weak 2-categories
10 Other definitions of weak n-category
10.1 Algebraic definitions
10.2 Non-algebraic definitions
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