Approximations and adjoints in homotopy categories

By Henning Krause. 2010

51 citations recorded by the source corpus.

We provide a criterion for the existence of right approximations in cocomplete additive categories; it is a straightforward generalisation of a result due to El Bashir. This criterion is used to construct adjoint functors in homotopy categories. Applications include the study of (pure) derived categories. For instance, it is shown that the pure derived category of any module category is compactly generated.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f0902b2984531c7122a772e8dab90830552475f1

How researchers see this paper

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In Algebra and Number Theory

1. J. Št’ovíček
2. Manuel Saor'in
3. Lidia Angeleri Hugel

In Mathematical Physics

1. J. Št’ovíček
2. Manuel Saor'in
3. Lidia Angeleri Hugel
4. L. Positselski
5. Jorge Vit'oria
6. James Gillespie
7. Chrysostomos Psaroudakis

Citations in the corpus

• On exact categories and applications to triangulated adjoints and model structures (2010, background): “Several versions of El Bashir’s result have appeared in the literature since then, to our best knowledge the most general of them being the one obtained in [40] by Krause.”