Algebraic Topology: Lecture 14

We further discussed the model category of simplicial sets. We defined the sets

   I = { d Delta[n]  --> Delta[n] | n >= 0 }
   J = { Lambda^r[n] --> Delta[n] | n >= 0, 0 =< r =< n }

of generators for the cofibrations and trivial cofibrations. We characterized the fibrant simplicial sets as those simplicial sets that satisfy the Kan extension condition. Finally, we formulated the definition of the Kan homotopy groups of a fibrant simplicial set.

We also formulated the following report problem.