Contents Abstract. viii Chapter 1. Introduction 1 Chapter 2. m-coalgebras 9 1. Preliminaries 9 2. Formal coalgebras 10 3. m-coalgebras 18 4. m-coalgebras and topological spaces 28 Chapter 3. The bar and cobar constructions 35 1. A (oo)-coalgebras 35 2. The Cobar Construction 38 3. The Bar Construction 60 4. Geometricity of the m-structure on the cobar construction 66 Chapter 4. Fibrations and twisted tensor products 69 1. The functors Yn|fn (91) 69 2. Approximate m-structures on twisted tensor products 86 3. Geometricity of the m-structure on a twisted tensor product 93 Appendices 99 A. Proof of 2.17 (on page 17) 99 B. A morphism from WX to B{X) 103 C. Proof of 2.12 (on page 43) 106 D. The maps {9ttn} 111 E. The composition-operations of Yn,m{%fy*k{t^i}?^, n) 117 F. Calculations 119 Bibliography 137
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