Talk:Derived category

Untitled
Shouldn't this article actually SAY what a derived category is?

Ahem...it does?136.152.132.18 21:33, 27 April 2007 (UTC)

Some comments
The first reference to springer's encyclopedia of math is broken. It should read http://www.encyclopediaofmath.org/index.php/Derived_category but I don't know how to update it. — Preceding unsigned comment added by 141.211.63.94 (talk) 14:09, 24 March 2012 (UTC)

The article says


 * This is the point where the homotopy category comes into play again: mapping an :object A of \mathcal A to (any) injective resolution I * of A defines a functor
 * D^+(\mathcal A) \rightarrow K^+(\mathrm{Inj}(\mathcal A))
 * from the bounded below derived category to the bounded below homotopy category of :complexes whose terms are injective objects in \mathcal A.
 * from the bounded below derived category to the bounded below homotopy category of :complexes whose terms are injective objects in \mathcal A.
 * from the bounded below derived category to the bounded below homotopy category of :complexes whose terms are injective objects in \mathcal A.

How is that? Mapping an object of \mathcal A to an injective resolution maps individual objects of \mathcal A, but the objects of D^+(\mathcal A) are chain complexes of objects of \mathcal A. I cannot see how one obtains the functor the text claims to obtain.

Also, it would be nice if the article explained the connection between hyperhomology and derived categories.87.93.226.24 (talk) 18:16, 31 May 2011 (UTC)


 * I reworded it slightly. Given a bounded above complex C, you take an injective resolution of each individual term. By the preceding paragraph, there are maps between these resolutions, so you get a double complex. The total complex of this still consists of injective objects. This is the image of C under the functor in question. Jakob.scholbach (talk) 19:10, 31 May 2011 (UTC)

Assessment comment
Substituted at 01:59, 5 May 2016 (UTC)

Additional Sections
This page should include expressions of hom sets through chain complexes and applications, such as the Atiyah class. — Preceding unsigned comment added by 207.109.53.162 (talk) 22:31, 17 December 2019 (UTC)