Monoidal Categories and Topological Field Theory: 322 (Progress in Mathematics) - Tapa dura

<P>THIS MONOGRAPH IS DEVOTED TO MONOIDAL CATEGORIES AND THEIR CONNECTIONS WITH 3-DIMENSIONAL TOPOLOGICAL FIELD THEORIES. STARTING WITH BASIC DEFINITIONS, IT PROCEEDS TO THE FOREFRONT OF CURRENT RESEARCH.</P>PART 1&NBSP;INTRODUCES MONOIDAL CATEGORIES AND SEVERAL OF THEIR CLASSES, INCLUDING RIGID, PIVOTAL, SPHERICAL, FUSION, BRAIDED, AND MODULAR CATEGORIES. IT THEN PRESENTS DEEP THEOREMS OF MÜGER ON THE CENTER OF A PIVOTAL FUSION CATEGORY. THESE THEOREMS ARE PROVED IN PART 2 USING THE THEORY OF HOPF MONADS. IN PART 3 THE AUTHORS DEFINE THE NOTION OF A TOPOLOGICAL QUANTUM FIELD THEORY (TQFT) AND CONSTRUCT A TURAEV-VIRO-TYPE 3-DIMENSIONAL STATE SUM TQFT FROM A SPHERICAL FUSION CATEGORY. LASTLY, IN PART 4 THIS CONSTRUCTION IS EXTENDED TO 3-MANIFOLDS WITH COLORED RIBBON GRAPHS, YIELDING A SO-CALLED GRAPH TQFT (AND, CONSEQUENTLY, A 3-2-1 EXTENDED TQFT). THE AUTHORS THEN PROVE THE MAIN RESULT OF THE MONOGRAPH: THE STATE SUM GRAPH TQFT DERIVED FROM ANY SPHERICAL FUSION CATEGORY IS ISOMORPHIC TO THE RESHETIKHIN-TURAEV SURGERY GRAPH TQFT DERIVED FROM THE CENTER OF THAT CATEGORY.<P></P><P>THE BOOK IS OF INTEREST TO RESEARCHERS AND STUDENTS STUDYING TOPOLOGICAL FIELD THEORY, MONOIDAL CATEGORIES, HOPF ALGEBRAS AND HOPF MONADS.</P><P> </P><P>&NBSP;</P>