  The present paper is devoted to study the homotopy category associated with a
simplicial descent category (D,s,E) (arXiv:0808.3684v2). We prove that the
class E of equivalences has a calculus of left fractions over a quotient
category of D modulo homotopy. We study the fiber/cofiber sequences induced by
a (co)simplicial descent structure. Examples of such fiber/cofiber sequences
are deduced for (commutative) differential graded algebras, simplicial sets or
topological spaces. We prove that the homotopy category of a stable simplicial
descent category is triangulated. In addition, these triangulated structures
may be extended to the homotopy categories of diagram categories of D. As a
corollary, we obtain the triangulated structures on: (filtered) derived
categories of abelian categories, the derived category of DG-modules over a
DG-category, the stable derived category of fibrant spectra and the localized
category of mixed Hodge complexes.
