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A morphism in the chosen cofibration class of a model category. In the projective model structure on nonnegative chain complexes it is a degreewise split injection with degreewise projective cokernel. This usage is distinguished from the topological cofibration.

A morphism in the chosen fibration class of a model category. In the projective model structure on nonnegative chain complexes, it is surjective in strictly positive degrees; degree zero is not required.

A morphism in the chosen weak-equivalence class of a model category. In the projective model structure on nonnegative chain complexes these are quasi-isomorphisms.

The model category of nonnegative complexes of left modules has quasi-isomorphisms as model weak equivalences, positive-degree surjections as model fibrations, and degreewise injections with projective cokernel as model cofibrations. All objects are fibrant; cofibrant objects are degreewise projective.