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short exact sequence
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English
Wikipedia
has an article on:
short exact sequence
Wikipedia
Diagram of a
short exact sequence
0
→
z
A
→
i
B
→
s
C
→
c
0
{\displaystyle 0{\xrightarrow {z}}A{\xrightarrow {i}}B{\xrightarrow {s}}C{\xrightarrow {c}}0}
; actually the diagram suggests a model thereof in category
S
e
t
{\displaystyle \mathbf {Set} }
(or any category that has a forgetful functor to
S
e
t
{\displaystyle \mathbf {Set} }
). Function
i
is an injection and function
s
a surjection. Function
c
is constant. The image
i
(
A
)
{\displaystyle i(A)}
equals
A’
, and
C
is isomorphic to the quotient
B
modulo
A’
.
Noun
edit
short
exact sequence
(
plural
short exact sequences
)
(
algebra
)
An
exact sequence
of precisely three
nontrivial
objects
(
e.g.
,
modules
).