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Any
-derivation
over
defines by restriction a
-derivation
over
which
we denote by
.
The rest is easy observation.
With the help of universality of
, we obtain the following corollary.
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ARRAY(0x9294884)
We assume that the assignment
In other words, we have
for any
holds for all
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We assume that the assignments
is natural.
Assume furthermore that for any
-module
, a sequence
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(which arises due to the claim above) is also exact.
Then for any
(2) Since
,
we deduce that
using the uniqueness of the
homomorphism which represents
.
For surjectivity of
, we use the sequence
for
.
For the exactness at the middle term,
we use the sequence
for
.
We leave the detail as an easy exercise.