The Inductive Coherator For Grothendieck Infinity Groupoids
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915576880824320 |
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| author | Taylor, Johnathon |
| author_facet | Taylor, Johnathon |
| contents | We extend the theory of distributive series of monads of \cite{EC1} by extending the definition to include an $\bN$-indexed collection of monads. Under certain conditions, distributive series of monads will have a colimit in the category of pointed endofunctors. We define a \emph{completable} distributive series of monads to be a distributive series of monads whose induced pointed endofunctor, if it exists, lifts to a monad. We then construct factorization systems used to generate monads on the category of theories over $Θ_0^\op$, in order to form two \emph{completable} distributive series of monads. The first completable distributive series of monads induces a monad that sends the identity theory over $Θ_0^\op$ to an $(\infty,0)$-coherator whose inductive construction mimics inductive weak enrichment. The second completable distributive series of monads induces a monad that sends the identity theory over $Θ_0^\op$ to a theory for strict $\infty$-groupoids. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_22326 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Inductive Coherator For Grothendieck Infinity Groupoids Taylor, Johnathon Category Theory 18A32, 18C15, 18N99, 18A20 We extend the theory of distributive series of monads of \cite{EC1} by extending the definition to include an $\bN$-indexed collection of monads. Under certain conditions, distributive series of monads will have a colimit in the category of pointed endofunctors. We define a \emph{completable} distributive series of monads to be a distributive series of monads whose induced pointed endofunctor, if it exists, lifts to a monad. We then construct factorization systems used to generate monads on the category of theories over $Θ_0^\op$, in order to form two \emph{completable} distributive series of monads. The first completable distributive series of monads induces a monad that sends the identity theory over $Θ_0^\op$ to an $(\infty,0)$-coherator whose inductive construction mimics inductive weak enrichment. The second completable distributive series of monads induces a monad that sends the identity theory over $Θ_0^\op$ to a theory for strict $\infty$-groupoids. |
| title | The Inductive Coherator For Grothendieck Infinity Groupoids |
| topic | Category Theory 18A32, 18C15, 18N99, 18A20 |
| url | https://arxiv.org/abs/2510.22326 |