arXiv subjects
Publications and source records attributed to Paratat Bejrakarbum.
We investigate the notion of involutive weak cubical $ω$-categories via Penon's approach: as algebras for the monad induced by the free involutive strict $ω$-category functor on cubical $ω$-sets. A few examples of involutive weak cubical $ω$-categories are provided.
We investigate the notion of involutive weak globular $ω$-categories via 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 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.
We investigate the notion of involutive weak globular $ω$-categories via Jacque Penon's approach. In particular, we give the constructions of a free self-dual globular $ω$-magma, of a free strict involutive globular $ω$-category, over an $ω$-globular set, and a contraction between them. The monadic definition of involutive weak globular $ω$-categories is given as usual via algebras for the monad induced by a certain adjunction. In our case, the adjunction is obtained from the "free functor" that associates to every $ω$-globular set the above contraction. Some examples of involutive weak globular $ω$-categories are also provided.