Comparing Composites of Left and Right Derived Functors
نویسنده
چکیده
We introduce a new categorical framework for studying derived functors, and in particular for comparing composites of left and right derived functors. Our central observation is that model categories are the objects of a double category whose vertical and horizontal arrows are left and right Quillen functors, respectively, and that passage to derived functors is functorial at the level of this double category. The theory of conjunctions and mates in double categories, which generalizes the theory of adjunctions in 2-categories, then gives us canonical ways to compare composites of left and right derived functors.
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