For each abelian category A, there is a category D(A), called the derived category of A, whose objects are complexes of objects of A, and whose morphisms are formal fractions of homotopy classes of complex morphisms having as denominators homotopy classes inducing isomorphisms in cohomology.
If F : A →B is an additive functor between
abelian categories, then under suitable conditions on A,
there is a functor RF : D(A) → D(B) with the property
that if objects X of A are considered as complexes concentrated at degree 0, then there are isomorphisms [formula omitted] for all n, where [formula omitted] is the ordinary [formula omitted] right derived functor of F. RF is called the derived functor of F, and one may look upon it as a kind of extension of F. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/33402 |
| Date | January 1971 |
| Creators | Loo, Donald Doo Fuey |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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