The Grothendieck spectral sequence computes the right derived functors of a composition of left exact functors 
and 
between Abelian categories. Assume 
and 
have enough injectives
and that 
for every injective object 
of 
and every 
. For an object 
of 
, it has
 |
with 
,
and induces a finite filtration
on each object 
(The Stacks Project Authors 2026). Here left
exact means preserving exactness at the first two
places of a short exact sequence. An object 
is an injective object when the hom
functor 
is exact, and enough injectives
means that every object embeds in such an 
. The Leray spectral
sequence is a sheaf-theoretic example.
