Mathematics – K-Theory and Homology
Scientific paper
2010-04-12
Math. Research Letters, Vol. 17, Issue 6 (2010)
Mathematics
K-Theory and Homology
Final version. Erroneous example in the introduction is removed
Scientific paper
Assume that abelian categories $A, B$ over a field admit countable direct limits and that these limits are exact. Let $F: D^+_{dg}(A) --> D^+_{dg}(B)$ be a DG quasi-functor such that the functor $Ho(F): D^+(A) \to D^+(B)$ carries $D^{\geq 0}(A)$ to $D^{\geq 0}(B)$ and such that, for every $i>0$, the functor $H^i F: A \to B$ is effaceable. We prove that $F$ is canonically isomorphic to the right derived DG functor $RH^0(F)$. We also prove a similar result for bounded derived DG categories in a more general setting. We give an example showing that the corresponding statements for triangulated functors are false. We prove a formula that expresses Hochschild cohomology of the categories $ D^b_{dg}(A)$, $ D^+_{dg}(A) $ as the $Ext$ groups in the abelian category of left exact functors $A \to Ind B$ .
No associations
LandOfFree
On the derived DG functors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the derived DG functors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the derived DG functors will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-262543