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Involutive Weak Globular $\omega$-categories
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abstract
We investigate the notion of involutive weak globular $\omega$-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 $\omega$-category functor on globular $\omega$-sets. An apparently more restrictive notion of involutive weak globular $\omega$-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.
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Cited by 1 Pith paper
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Involutive Weak Cubical $\omega$-categories
The authors introduce involutive weak cubical omega-categories as monad algebras and prove the free constructions needed for that definition exist.
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