High Quality Content by WIKIPEDIA articles! A category C is equipped with bifibrations if it has cofibrations and its opposite category COP has so also. In that case, we denote the fibrations of COP by quot(C). In that case, C is a biWaldhausen category if C has bifibrations and weak equivalences such that both (C, co(C), we) and (COP, quot(C), weOP) are Waldhausen categories. As examples one may think of exact categories, where the cofibrations are the admissible monomorphisms. Another example is model categories, though they have much more structure than needed.

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