Enriched Multicategories and Multiequivalences

This chapter discusses enriched multicategories and contains the first main theorem of this monograph. It first recalls the 2-category of small V-multicategories, V-multifunctors, and V-multinatural transformations for a symmetric monoidal category V. The second half of this chapter is devoted to the local characterization of adjoint Cat-multiequivalences. The usual local characterization of 2-equivalences is a special case of this theorem.