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 |
|---|---|
| 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