Involutive Weak Globular $ω$-categories
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866918130967642112 |
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| author | Bejrakarbum, Paratat Bertozzini, Paolo |
| author_facet | Bejrakarbum, Paratat Bertozzini, Paolo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_16419 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Involutive Weak Globular $ω$-categories Bejrakarbum, Paratat Bertozzini, Paolo Category Theory Operator Algebras 18N65 (Primary) 18N70, 18M40, 18N30, 18N99 (Secondary) 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. |
| title | Involutive Weak Globular $ω$-categories |
| topic | Category Theory Operator Algebras 18N65 (Primary) 18N70, 18M40, 18N30, 18N99 (Secondary) |
| url | https://arxiv.org/abs/2303.16419 |