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Contents xxi

Appendix III: Elliptic Curves and Topological Modular Forms .......... 425
1 Categories in a Category. . . .................................. 427
2 Groupoids in a Category . . . .................................. 429
3 Cocategories over Commutative Algebras: Hopf Algebroids . . ..... 431
4 The Category WT(R) and the Weierstrass Hopf Algebroid ......... 434
5 Morphisms of Hopf Algebroids: Modular Forms ................ 438
6 The Role of the Formal Group in the Relation Between Elliptic
Curves and General Cohomology Theory ...................... 441
7 The Cohomology Theory or Spectrum tmf...................... 443
References ..................................................... 444

Appendix IV: Guide to the Exercises ................................ 445
Ruth Lawrence

References ...................................................... 465
List of Notation .................................................. 479

Index ........................................................... 481