`Algebraic Models of $(\infty,n)$-categories on the globular setting'

Camell Kachour
 
In this talk we define a sequence of monads T^{(\infty,n)} (n in N) 
on the category of globular sets. We conjecture that algebras for T^{(\infty,0)}, 
which are defined in a purely algebraic setting, are models of \infty-groupoids. 
A sequence of monads T^{(\infty,n)} on the category of globular sets is defined 
with the conjectural property that T^{(\infty,n)}-algebras are models for 
(\infty,n)-categories. Our models of \infty-groupoids might solved the 
"Grothendieck conjecture on homotopy types" (Probably in the future 
thesis of Rémy Tuyéras, Macquarie University)