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I am splitting off homotopy category of a model category from model category. Have spelled out statement and proof of the localization construction there.
I have also added a section Derived functors spelling out statement and proof of some basic facts.
In the course of this I touched other relevant entries. For instance to Quillen adjunction I added the proof that the various equivalent ways to state the conditions are indeed equivalent. Still need to type out the analogue for Quillen equivalences.
added to the section on derived functors statement of the derived adjunction of a Quillen adjunction
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