Donald Yau is a Professor of Mathematics at The Ohio State University at Newark, specializing in homotopy theory and algebraic K-theory. He obtained his PhD at MIT under the direction of Haynes Miller and held a post-doctoral position at the University of Illinois at Urbana-Champaign. He is the author of over fifty research articles and ten books.

• Chapter 1. Preliminaries on Enriched Categories and 2-Categories. Chapter 2, Symmetric Bimonoidal and Bipermutative Categories. Chapter 3. Enriched Multicategories and Multiequivalences. Chapter 4. Pseudo Symmetry. Chapter 5. Enriched Multicategories of Indexed Categories. Chapter 6. The Grothendieck Construction is a Pseudo Symmetric Cat-Multifunctor. Chapter 7. Permutative Opfibrations from Bipermutative-Indexed Categories. Chapter 8. The Grothendieck Construction is a Cat-Multiequivalence. Chapter 9. The Cat-Multifunctor A. Chapter 10. Inverse K-Theory is a Pseudo Symmetric Cat-Multifunctor.

Donald Yau is a Professor of Mathematics at The Ohio State University at Newark, specializing in homotopy theory and algebraic K-theory. He obtained his PhD at MIT under the direction of Haynes Miller and held a post-doctoral position at the University of Illinois at Urbana-Champaign. He is the author of over fifty research articles and ten books.

• Chapter 1. Preliminaries on Enriched Categories and 2-Categories. Chapter 2, Symmetric Bimonoidal and Bipermutative Categories. Chapter 3. Enriched Multicategories and Multiequivalences. Chapter 4. Pseudo Symmetry. Chapter 5. Enriched Multicategories of Indexed Categories. Chapter 6. The Grothendieck Construction is a Pseudo Symmetric Cat-Multifunctor. Chapter 7. Permutative Opfibrations from Bipermutative-Indexed Categories. Chapter 8. The Grothendieck Construction is a Cat-Multiequivalence. Chapter 9. The Cat-Multifunctor A. Chapter 10. Inverse K-Theory is a Pseudo Symmetric Cat-Multifunctor.

Donald Yau is a Professor of Mathematics at The Ohio State University at Newark, specializing in homotopy theory and algebraic K-theory. He obtained his PhD at MIT under the direction of Haynes Miller and held a post-doctoral position at the University of Illinois at Urbana-Champaign. He is the author of over fifty research articles and ten books.

• Chapter 1. Preliminaries on Enriched Categories and 2-Categories. Chapter 2, Symmetric Bimonoidal and Bipermutative Categories. Chapter 3. Enriched Multicategories and Multiequivalences. Chapter 4. Pseudo Symmetry. Chapter 5. Enriched Multicategories of Indexed Categories. Chapter 6. The Grothendieck Construction is a Pseudo Symmetric Cat-Multifunctor. Chapter 7. Permutative Opfibrations from Bipermutative-Indexed Categories. Chapter 8. The Grothendieck Construction is a Cat-Multiequivalence. Chapter 9. The Cat-Multifunctor A. Chapter 10. Inverse K-Theory is a Pseudo Symmetric Cat-Multifunctor.