In this paper we define a sequence of monads T(∞, n)(n ε N) on the category ∞-Gr of ∞-graphs. We conjecture that algebras for T(∞, 0), which are defined in a purely algebraic setting, are models of ∞-groupoids. More generally, we conjecture that T(∞;n)-algebras are models for (∞, n)-categories. We prove that our (∞, 0)-categories are bigroupoids when truncated at level 2.
|Number of pages||33|
|Journal||Theory and Applications of Categories|
|Publication status||Published - 2015|
- Homotopy types
- Weak ∞-groupoids