Cisinski on homotopy theory in toposes. See also other papers by Cisinski.
Cox: Homotopy limits and the homotopy type of functor categories (1976) http://www.ams.org/mathscinet-getitem?mr=0407022
Jardine on the ideas of Cisinski
Anderson: Axiomatic homotopy theory (1978)
nLab page on Abstract homotopy theory