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.
