Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from areas as diverse as topology, quantum algebra, mathematical physics, logic, and theoretical computer science. The heart of this book is the language of generalized operads. This is as natural and transparent a language for higher category theory as the language of sheaves is for algebraic geometry, or vector spaces for linear algebra. It is introduced carefully, then used to give simple descriptions of a variety of higher categorical structures. In particular, one possible definition of n-category is discussed in detail, and some common aspects of other possible definitions are established. This is the first book on the subject and lays its foundations. It will appeal to both graduate students and established researchers who wish to become acquainted with this modern branch of mathematics.... with contraction n-leafed corolla product fundamental n-groupoid of space fundamental I-groupoid of space right unit isomorphism ... 0 objects of (multi) category 304 292 285 366 y 32, 50 93, 122 115 241 223 320 342 311 264 93, 122 244 274 32 ... 140 ( ) action of multicategory on algebra 65, 69, 275 ( ) mate 186 I ( ) globular set representing pasting diagram 269 ... algebras into multicategories 40, 185, 207, 208 ( ) 149 A(A, B) C(a1 , ..., a n; a) C((ax) xaX; b) abi 420 Index of notation.
|Title||:||Higher Operads, Higher Categories|
|Publisher||:||Cambridge University Press - 2004-07-22|