Abstract
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 |
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Keywords
- n-category
- higher dimensional category
- monad interleaving
- monad
- operad
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology
Cite this
A study of Penon weak n-categories Part 1: Monad interleaving. / Cottrell, Thomas.
In: Cahiers de Topologie et Géométrie Différentielle Catégoriques, Vol. LIX, No. 3, 01.01.2018, p. 197-259.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A study of Penon weak n-categories Part 1: Monad interleaving
AU - Cottrell, Thomas
PY - 2018/1/1
Y1 - 2018/1/1
N2 - We give an alternative construction of the monad used by Penonto define weak n-categories. Penon’s monad adds two pieces of extra structureto an n-globular set: a magma structure, giving composition, and a contractionstructure, giving coherence. We add these two structures using aninterleaving approach, following the method used by Cheng to construct Leinster’soperad for weak ω-categories. We conclude by using our constructionto give an explicit description of the n-globular operad for Penon weakn-categories.
AB - We give an alternative construction of the monad used by Penonto define weak n-categories. Penon’s monad adds two pieces of extra structureto an n-globular set: a magma structure, giving composition, and a contractionstructure, giving coherence. We add these two structures using aninterleaving approach, following the method used by Cheng to construct Leinster’soperad for weak ω-categories. We conclude by using our constructionto give an explicit description of the n-globular operad for Penon weakn-categories.
KW - n-category
KW - higher dimensional category
KW - monad interleaving
KW - monad
KW - operad
M3 - Article
VL - LIX
SP - 197
EP - 259
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
JF - Cahiers de Topologie et Géométrie Différentielle Catégoriques
SN - 1245-530X
IS - 3
ER -