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I have a further comment/question in the query box at category with weak equivalences
replied.
I have incorporated the query discussion at category with weak equivalences into the main text and deleted the query box. I also added some remarks about additional conditions on the weak equivalences.
Does anyone have a reference for where a category with weak equivalences was first defined?
Completed the John Bourke reference, and added a reference to Homotopy Limit Functors on Model Categories and Homotopical Categories where a category with weak equivalences is defined.
How about we say, concerning DHKS04, something like that:
The terminology and maybe the notion of “category with weak equivalences” may be due to:…
Because the basic idea sort of occurred before DHKS04, they may be the first to give it a concrete name and specific definition..
For example, the entry relative category cites Dwyer & Kan 1980 for the notion of “relative category”. With the same justification one could attribute “category with weak equivalences” to them: They don’t explicitly write either of these terms, but are clearly using the respective idea.
Sounds good to me! Thanks for adding the additional context.
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