Pathway XXIX

sSetSimplicial sets and model categories

Simplices glued along faces. Horns that fillers turn into homotopies. Quillen’s model structure.

1. 01Simplicial setsA simplicial set assigns a set of n-simplices to each n, with face and degeneracy maps.4 min
2. 02Model categoriesWeak equivalences, fibrations, cofibrations. A homotopy theory with lifting axioms.4 min
3. 03Simplicial homologyAlgebraic topology: count holes by making a chain complex from simplices, then taking ker ∂ / im ∂.4 min