Abstract
We give an alternative construction of the monad used by Penon
to define weak n-categories. Penon’s monad adds two pieces of extra structure
to an n-globular set: a magma structure, giving composition, and a contraction
structure, giving coherence. We add these two structures using an
interleaving approach, following the method used by Cheng to construct Leinster’s
operad for weak ω-categories. We conclude by using our construction
to give an explicit description of the n-globular operad for Penon weak
n-categories.
to define weak n-categories. Penon’s monad adds two pieces of extra structure
to an n-globular set: a magma structure, giving composition, and a contraction
structure, giving coherence. We add these two structures using an
interleaving approach, following the method used by Cheng to construct Leinster’s
operad for weak ω-categories. We conclude by using our construction
to give an explicit description of the n-globular operad for Penon weak
n-categories.
Original language | English |
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Pages (from-to) | 197-259 |
Number of pages | 63 |
Journal | Cahiers de Topologie et Géométrie Différentielle Catégoriques |
Volume | LIX |
Issue number | 3 |
Publication status | Published - 1 Jan 2018 |
Keywords
- n-category
- higher dimensional category
- monad interleaving
- monad
- operad
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology