Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

In $k$-linear triangulated categories, there is an evaluation map

$$\oplus_i \text{Hom}(E,A[i])\otimes_k E[-i]\to A .$$

I've learned that in the derived categorie of coherent sheafs on a scheme $X$, the tensor product $V\otimes F[-i]$ is just the direct sum of $\text{dim }V$ copies of $F[-i]$.

However, I do not understand the above construction in general triangulated $k$-linear categories. Could anyone help me to understand how the tensorproduct and the evaluation map are defined? Thank you.

share|improve this question
    
Looking at Bondal "Representation of associative algebras and coherent sheaves " suggests that the $\text{coh X}$ case is the general definition, not a consequence. –  Carsten Jan 18 '12 at 11:45
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.