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The HomotopyCategories package is a Gap/CAP package written for
constructing homotopy categories of additive categories, i.e., the
category of complexes modulo null-homotopic morphisms. Its aim is to
carry out categorical and homological constructions and
computations. Homotopy categories are in many cases a nice model for
derived categroies. For example, when the category has enough
injectives or enough projectives. This package has been written as
step toward implementing derived categories and Tilting equivalences
between them.