Abstract
In this paper we take the first step towards a comparison between
an algebraic and a non-algebraic definition of weak n-category. This comparison takes the form of a nerve functor, the established method of moving from the algebraic setting to the non-algebraic setting. The algebraic definition we use is that due to Penon, and the non-algebraic definition we use is Simpson’s variant of Tamsamani’s definition. As a prototype for our nerve
construction, we recall a nerve construction for bicategories proposed by Leinster, and prove that the nerve of a bicategory given by this construction is
a Tamsamani–Simpson weak 2-category. We then define our nerve functor
for Penon weak n-categories. We prove that the nerve of a Penon weak 2-
category is a Tamsamani–Simpson weak 2-category, and conjecture that this
result holds for higher n.
an algebraic and a non-algebraic definition of weak n-category. This comparison takes the form of a nerve functor, the established method of moving from the algebraic setting to the non-algebraic setting. The algebraic definition we use is that due to Penon, and the non-algebraic definition we use is Simpson’s variant of Tamsamani’s definition. As a prototype for our nerve
construction, we recall a nerve construction for bicategories proposed by Leinster, and prove that the nerve of a bicategory given by this construction is
a Tamsamani–Simpson weak 2-category. We then define our nerve functor
for Penon weak n-categories. We prove that the nerve of a Penon weak 2-
category is a Tamsamani–Simpson weak 2-category, and conjecture that this
result holds for higher n.
| Original language | English |
|---|---|
| Pages (from-to) | 32-114 |
| Journal | Cahiers de Topologie et Géométrie Différentielle Catégoriques |
| Volume | LX |
| Issue number | 1 |
| Publication status | Published - 2019 |
Keywords
- n-category
- higher-dimensional category
- nerve construction
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology