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  • For every cofibrant object c???Cc\in C, the composite c???R(L(c))???R(L(c) fib)c o R(L(c)) o R(L(c)^{fib}) is a weak equivalence in CC, and for every fibrant object d???Dd\in D, the composite L(R(d) cof)???L(R(d))???dL(R(d)^{cof}) o L(R(d)) o d is a weak equivalence in DD, where (???) fib(-)^{fib} and (???) cof(-)^{cof} denote fibrant and cofibrant resolutions, respectively.
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