Simplicial homotopy theory is the study of homotopy theory by means of simplicial sets, but also the study of those properties of simplicial sets detectable by means of techniques adapted from topological homotopy theory.
homotopy hypothesis-theorem
Pierre Gabriel, Michel Zisman, Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35. Springer, New York (1967)
Edward Curtis, Simplicial Homotopy Theory, Advances in Math., 6, (1971), 107 – 209.
Paul Goerss, Rick Jardine, Simplicial homotopy theory, Progress in Mathematics, Birkhäuser (1996)