Derived, coderived, and contraderived categories of locally presentable abelian categories

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00545361" target="_blank" >RIV/67985840:_____/22:00545361 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/22:10452303
Result on the web
<a href="https://doi.org/10.1016/j.jpaa.2021.106883" target="_blank" >https://doi.org/10.1016/j.jpaa.2021.106883</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpaa.2021.106883" target="_blank" >10.1016/j.jpaa.2021.106883</a>

Result language
angličtina
Original language name
Derived, coderived, and contraderived categories of locally presentable abelian categories
Original language description
For a locally presentable abelian category B with a projective generator, we construct the projective derived and contraderived model structures on the category of complexes, proving in particular the existence of enough homotopy projective complexes of projective objects. We also show that the derived category D(B) is generated, as a triangulated category with coproducts, by the projective generator of B. For a Grothendieck abelian category A, we construct the injective derived and coderived model structures on complexes. Assuming Vopěnka’s principle, we prove that the derived category D(A) is generated, as a triangulated category with products, by the injective cogenerator of A. We also define the notion of an exact category with an object size function and prove that the derived category of any such exact category with exact κ-directed colimits of chains of admissible monomorphisms has Hom sets. Hence the derived category of any locally presentable abelian category has Hom sets.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA20-13778S" target="_blank" >GA20-13778S: Symmetries, dualities and approximations in derived algebraic geometry and representation theory</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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