Derived Category VT26

Here are the last rules (I had forgot one)

5) $X'\xrightarrow{f}X\xrightarrow{g} X''$ is exact iff $g\circ f=0$ and for all $y\in X$ with $g(y)=0$ there is a $z\in X'$ with $f(z)=y$.

6) given a generalized element $y=[Y,h]$ we denote by $-y=[Y,-h]$. Suppose $g:X\rightarrow Z$ is a morphism and there are two elements of $X$ such that $g(x)=g(x')$. Then there is an element of $z\in X$  with $g(z)=0$ and for all $f:X\rightarrow T$ with $f(x)=0$ we have that $f(z)=-f(x')$ and for all $f':X\rightarrow T$ with $f'(x')=0$ we have that $f'(z)=f'(x)$.