ScalingStacks

Proposition 21 We have direct sum decompositions

	$\displaystyle\overline{C}(D_{1})$	$\displaystyle=$	$\displaystyle X_{1}\oplus X_{2}\oplus X_{3}$		(129)
	$\displaystyle\overline{C}(D_{2})$	$\displaystyle=$	$\displaystyle Y_{1}\oplus Y_{2}\oplus Y_{3}$		(130)

The complexes $X_{2},X_{3},Y_{2}$ and $Y_{3}$ are acyclic.

The complexes $X_{1}$ and $Y_{1}$ are isomorphic.