Involutive Weak Globular $\omega$-categories

Paratat Bejrakarbum; Paolo Bertozzini

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arXiv · 2303.16419

Involutive Weak Globular $\omega$-categories

Paratat Bejrakarbum·Paolo Bertozzini

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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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Paratat Bejrakarbum, Paolo Bertozzini. 2023-03-29. Involutive Weak Globular $\omega$-categories. https://arxiv.org/abs/2303.16419

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