Contents

• Cyclic category
  • Circle and disk as a cell complexes
  • Simplicial sets
  • Fibrations
  • Cyclic category
  • Noncommutative sets
  • Adjoint functors
  • Generic example of a simplicial set
  • Simplicial modules
  • Bicomplexes
  • Spectral sequences
  
  
• Cyclic homology
  • The cyclic bicomplex
  • Characteristic 0 case
  • Computations
  • Periodic and negative cyclic homology
  • Harrison homology
  • Derived functors
  
  
• Relation with K-theory
  • K-theory
  • Trace map
  • Algebraic K-theory