Let $$ \begin{array}{rcl} A&\to& B\\ \downarrow & &\downarrow\\ A’&\to& B’ \end{array} $$ be a commutative diagram in a triangulated category. By the axioms of a triangulated category, this may be ‘completed’ to $$ \begin{array}{rccccl} A&\to& B&\to& C&\to\\ \downarrow & &\downarrow&&\downarrow\\ A’&\to& B’&\to& C’&\to \end{array} $$ where both rows are exact triangles. Let $$ \begin{array}{rccccl} A&\to& […]

I read in the book Methods of homological algebra of Gelfand and Manin that the derived category of an abelian category $A$ is never abelian. Now to me this seems to be wrong, because if $A=0$ then $D(A)=0$ and so it is abelian. Do you know what statement is true? (Like every derived category of […]

Intereting Posts

conversion of laplacian from cartesian to spherical coordinates
Order of element equal to least common multiple
How to get the minimum and maximum of one convex function?
Is there such thing as an unnormed vector space?
What is the topology of the hyperreal line?
What is a way to do this combinatorics problem that could generalize to do any of problems similar to this but with more path?
Irrational roots of unity?
Centre in N-sided polygon on circle
Proof for divisibility rule for palindromic integers
Does every nonempty definable finite set have a definable member?
Measure spaces s.t. $\mathcal{L}^1 = L^1$
Why is the sum of residues of $\frac{1}{1+z^n}$ in the upper half plane $1/$?
Group of even order contains an element of order 2
Show that 7 is a quadratic residue for any prime p of the form 28k + 1 and 28k + 3.
Solving contour integral