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Dec 13, 2019 at 16:44 comment added John Klein It is the best I can do. Unfortunately the literature on this topic is not complete.
Dec 13, 2019 at 14:58 comment added Ivan Di Liberti Thanks, but your Remark is essentially only stating that the result is true, which I believe, and is indicating the correct ingredients to cook a theorem (the theory of framings) which is mentioned in several sources. Yet, it is very far from providing an answer to the question. That is, is there any reference?
Dec 13, 2019 at 13:42 comment added John Klein @IvanDiLiberti Please see my edit.
Dec 13, 2019 at 13:42 history edited John Klein CC BY-SA 4.0
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Dec 13, 2019 at 13:07 comment added John Klein I agree, I failed to address that issue. Although I have no reference, I do not think that the failure of having functorial factorizations will affect the answer to Q2.
Dec 13, 2019 at 13:03 history edited John Klein CC BY-SA 4.0
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Dec 13, 2019 at 13:02 comment added Ivan Di Liberti For the interested reader, let me observe that in II.9.1 of the aforementioned book, they specify that the factorization systems are functorial, while I specified that I would like to avoid this assumption. For this reason, this answer will not be accepted.
Dec 13, 2019 at 12:53 history edited John Klein CC BY-SA 4.0
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Dec 13, 2019 at 12:42 history answered John Klein CC BY-SA 4.0