Colored operads:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2016]
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| Schriftenreihe: | Graduate studies in mathematics
170 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xxviii, 428 Seiten Diagramme |
| ISBN: | 9781470427238 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804176014114291712 |
|---|---|
| adam_text | Titel: Colored operads
Autor: Yau, Donald
Jahr: 2016
Contents Preface xiii Acknowledgments xxi List of Notations xxiii Part 1. Graphs and Trees Chapter 1. Directed Graphs 3 §1.1. Set Notations 3 §1.2. Graphs 5 §1.3. Directed Graphs 8 §1.4. Directed (m,n)-Graphs 10 §1.5. Exercises 16 §1.6. Notes 17 Chapter 2. Extra Structures on Graphs 19 §2.1. Edge Coloring 19 §2.2. Vertex Decoration 20 §2.3. Input Labeling 21 §2.4. Incoming Edge Labeling 24 §2.5. Isomorphisms with Extra Structures 26 §2.6. Exercises 27
Contents viii Chapter 3. Rooted Trees §3.1. Rooted Trees §3.2. Profile of a Vertex §3.3. Profile of a Rooted Tree §3.4. Exceptional Edge and Corollas §3.5. Simple Trees §3.6. Level Trees §3.7. Linear Graphs §3.8. Exercises Chapter 4. Collapsing an Internal Edge §4.1. Motivation §4.2. Defining the Quotient §4.3. Examples §4.4. Associativity §4.5. Compatibility with Extra Structures §4.6. Exercises Chapter §5.1. §5.2. §5.3. §5.4. §5.5. §5.6. §5.7. §5.8. 5. Grafting of Rooted Trees Motivation Defining Grafting Examples Unity Horizontal Associativity Vertical Associativity Grafting Decomposition of Rooted Trees Exercises Chapter § 6 . 1 . § 6 . 2 . §6.3. §6.4. §6.5. § 6 . 6 . §6.7. 6. Grafting and Extra Structures Edge Coloring Vertex Decoration Input Labeling Incoming Edge Labeling Canonical Vertex Labeling Canonical Input Labeling Exercises 29 30 31 31 32 34 36 40 40 43 43 44 46 48 48 51 53 54 55 57 60 62 64 66 72 75 75 76 77 79 80 82 85
Contents IX Part 2. Category Theory Chapter 7. Basic Category Theory §7.1. Categories §7.2. Functors §7.3. Natural Transformations §7.4. Equivalence §7.5. Coproducts §7.6. Products §7.7. Adjoint Functors §7.8. Exercises §7.9. Notes Chapter 8. Symmetric Monoidal Categories §8.1. Motivation for Monoidal Categories §8.2. Monoidal Categories §8.3. Monoidal Functors §8.4. Mac Lane’s Theorem §8.5. Symmetry §8.6. Permuting Iterated Tensor Products §8.7. Symmetric Monoidal Closed Categories §8.8. Standing Categorical Assumptions §8.9. Exercises §8.10. Notes Chapter 9. Colored Symmetric Sequences and Objects §9.1. Colors and Profiles §9.2. Permutation Category §9.3. Colored Symmetric Sequences §9.4. Colored Objects §9.5. Exercises §9.6. Notes Part 3. Operads and Algebras Chapter 10. Motivation for Colored Operads §10.1. Categories via Linear Graphs §10.2. Colored Operads via Trees 89 90 98 100 105 107 109 111 116 119 121 121 122 125 128 130 132 135 137 139 140 141 141 143 147 153 156 158 161 161 164
X Contents Chapter 11. Colored Operads §11.1. Block Permutations and Block Sums §11.2. Defining Colored Operads §11.3. Examples of the Axioms §11.4. Initial and Terminal Colored Operads §11.5. Changing the Base Category §11.6. 1-Colored Operads §11.7. Colored Non-Symmetric Operads §11.8. Exercises §11.9. Notes Chapter 12. Operads in Arity 1 §12.1. Motivation for Monoids §12.2. Monoids §12.3. Small Enriched Categories §12.4. Exercises Chapter 13. Algebras over Colored Operads §13.1. Motivation §13.2. Defining Algebras §13.3. Examples of the Axioms §13.4. Visualizing Algebras §13.5. Algebras over a 1-Colored Operad §13.6. Algebras over a Colored Non-Symmetric Operad §13.7. Motivation for Endomorphism Operads §13.8. Colored Endomorphism Operads §13.9. Algebra as a Map §13.10. Exercises §13.11. Notes Chapter 14. Examples of Algebras §14.1. Initial and Terminal Algebras §14.2. Operad for Monoids §14.3. Colored Operad for Monoid Maps §14.4. Colored Operad for Colored Monoids §14.5. Exercises 173 173 175 181 185 190 193 197 198 200 203 203 205 208 212 215 215 217 219 221 222 224 225 226 231 232 235 237 237 239 246 253 258
Contents xi Chapter 15. Motivation for Partial Compositions §15.1. Simplifying the Operadic Composition §15.2. Operadic Composition to Partial Composition §15.3. Partial Composition to Operadic Composition §15.4. Associativity §15.5. Unity §15.6. Equi variance Chapter 16. Colored Pseudo-Operads §16.1. Partial Compositions of Profiles §16.2. Defining Colored Pseudo-Operads §16.3. Examples of the Axioms §16.4. Colored Pseudo-Operads Are Colored Operads §16.5. 1-Colored Pseudo-Operads §16.6. Colored Non-Symmetric Pseudo-Operads §16.7. Algebras via Partial Compositions §16.8. Rooted Trees Operad §16.9. Little Square Operad §16.10. Exercises §16.11. Notes Part 4. Free Colored Operads Chapter 17. Motivation for Free Colored Operads §17.1. Free Monoids §17.2. Heuristic Free Colored Non-Symmetric Operads §17.3. Heuristic Free Colored Operads §17.4. Exercises Chapter 18. General Operadic Composition §18.1. Decoration by a Colored Object §18.2. Defining General Operadic Composition §18.3. Associativity §18.4. Exercises Chapter 19. Free Colored Non-Symmetric Operads §19.1. Entries and Structure Maps §19.2. Colored Non-Symmetric Operad Structure 265 265 267 270 271 272 273 275 275 278 285 289 293 296 298 301 305 309 317 321 321 327 330 332 333 333 340 347 350 351 352 357
Contents xii §19.3. The Adjunction 361 §19.4. Motivation for Tree Operads 370 §19.5. Colored Non-Symmetric Operad Generated by a Tree 372 §19.6. Exercises 379 Chapter 20. Free Colored Operads 381 §20.1. Colored Non-Symmetric Operads to Colored Operads 382 §20.2. Symmetrization 389 §20.3. Free Colored Operad of a Colored Object 394 §20.4. Colored Operad Generated by a Tree 404 §20.5. Exercises 408 Further Reading 409 Bibliography 413 List of Main Facts 419 Index 423
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| language | English |
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| spelling | Yau, Donald 1977- Verfasser (DE-588)141581875 aut Colored operads Donald Yau Operads Providence, Rhode Island American Mathematical Society [2016] © 2016 xxviii, 428 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 170 Operade (DE-588)4638722-5 gnd rswk-swf Operade (DE-588)4638722-5 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-2871-6 Graduate studies in mathematics 170 (DE-604)BV009739289 170 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028838630&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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