Remark 17.1.6. By combining the previous proposition with Proposition 17.1.3, we conclude that the class \(\Rr \) is automatically closed under retracts, base change, and left cancellation. Similarly, \(\Ll \) is closed under retracts, cobase change, and right cancellation.
In the literature, the condition that \(\Ll \) and \(\Rr \) need to be closed under retracts is often taken as part of the definition of a factorization system, but the previous proposition shows this assumption is redundant.
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