“…Recently, folds gained further prominence in connection with Hom complexes. One has discovered, see [Ba05], that it is possible to introduce a natural Quillen model category structure, see [GM96, Chapter V], and [Qu73], on the category of graphs, such that the weak equivalences are precisely the maps, which allow factorizations into a sequence of folds and unfolds (which therefore may be viewed as trivial homotopy equivalences).…”