Involutive Weak Globular !-categories

Abstract

We investigate the notion of involutive weak globular !-categories making use of T.Leinster’s approach: as algebras for the initial contracted globular operad in the bicategory of globular collections induced by the Cartesian monad of the free involutive strict !-category functor on globular !-sets. An apparently more restrictive notion of involutive weak globular !-categories as algebras for the initial operadic-contraction in the bicategory of globular contracted-collections induced by the previous Cartesian monad (where here the operadic multiplications and units satisfy further compatibility axioms with the contractions) is also considered.