INVOLUTIVE WEAK GLOBULARω-CATEGORIES

Abstract

We investigate the notion of
involutive
weak globular
ω
-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
ω
-category functor on globular
ω
-sets. An apparently more
restrictive notion of involutive weak globular
ω
-categories as algebras for the ini-
tial
operadic-contraction
in the bicategory of globular
contracted-collections
in-
duced by the previous Cartesian monad (where here the operadic multiplications
and units satisfy further compatibility axioms with the contractions) is also con-
sidered