Contents
Introduction 1
Chapter I. Prologue: the category of L-spectra 9
1. Background on spectra and the stable homotopy category 9
2. External smash products and twisted half-smash products 11
3. The linear isometries operad and internal smash products 13
4. The category of L-spectra 17
5. The smash product of L-spectra 20
6. The equivalence of the old and new smash products 22
7. Function L-spectra 25
8. Unital properties of the smash product of L-spectra 28
Chapter II. Structured ring and module spectra 31
1. The category of 5-modules 31
2. The mirror image to the category of 5-modules 35
3. 5-algebras and their modules 37
4. Free ^4^ and EQQ ring spectra; comparisons of definitions 39
5. Free modules over A^ and E^ ring spectra 42
6. Composites of monads and monadic tensor products 44
7. Limits and colimits of 5-algebras 47
Chapter III. The homotopy theory of i?-modules 51
1. The category of i?-modules; free and cofree i^-modules 51
2. Cell and CW i?-modules; the derived category of i2-modules 54
3. The smash product of /^-modules 58
4. Change of 5-algebras; g-cofibrant 5-algebras 61
5. Symmetric and extended powers of R-modules 64
6. Function it!-modules 65
7. Commutative 5-algebras and duality theory 69
Chapter IV. The algebraic theory of i^-modules 71
1. Tor and Ext; homology and cohomology; duality 71
2. Eilenberg-Mac Lane spectra and derived categories 74
3. The Atiyah-Hirzebruch spectral sequence 78
4. Universal coefficient and Kunneth spectral sequences 81
5. The construction of the spectral sequences 83
6. Eilenberg-Moore type spectral sequences 86
7. The bar constructions B(M, R, N) and B(X, G, Y) 88
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