2021
Gneri, P. O.; Jardim, Marcos; Silva, D. D.
Derived categories of functors and quiver sheaves Journal Article
Em: Journal of Algebra and Its Applications, vol. 21, iss. 7, 2021.
Resumo | Links | BibTeX | Tags: derived category of functors, Quiver sheaves
@article{nokey,
title = {Derived categories of functors and quiver sheaves},
author = {P. O. Gneri and Marcos Jardim and D. D. Silva},
url = {https://www.worldscientific.com/doi/10.1142/S0219498822501274},
doi = {https://doi.org/10.1142/S0219498822501274},
year = {2021},
date = {2021-03-19},
journal = {Journal of Algebra and Its Applications},
volume = {21},
issue = {7},
abstract = {Let C be small category and A an arbitrary category. Consider the category C(A) whose objects are functors from C to A and whose morphisms are natural transformations. Let B be another category, and again, consider the category C(B). Now, given a functor F:A→B we construct the induced functor FC:C(A)→C(B). Assuming A and B to be abelian categories, it follows that the categories C(A) and C(B) are also abelian. We have two main goals: first, to find a relationship between the derived category D(C(A)) and the category C(D(A)); second relate the functors R(FC) and (RF)C:C(D(A))→C(D(B)). We apply the general results obtained to the special case of quiver sheaves.},
keywords = {derived category of functors, Quiver sheaves},
pubstate = {published},
tppubtype = {article}
}
Let C be small category and A an arbitrary category. Consider the category C(A) whose objects are functors from C to A and whose morphisms are natural transformations. Let B be another category, and again, consider the category C(B). Now, given a functor F:A→B we construct the induced functor FC:C(A)→C(B). Assuming A and B to be abelian categories, it follows that the categories C(A) and C(B) are also abelian. We have two main goals: first, to find a relationship between the derived category D(C(A)) and the category C(D(A)); second relate the functors R(FC) and (RF)C:C(D(A))→C(D(B)). We apply the general results obtained to the special case of quiver sheaves.