In mathematics, a magma object, can be defined in any category
C
equipped with a distinguished bifunctor
⊗
:
C
×
C
→
C
. Since Mag, the category of magmas, has cartesian products, ergo we can consider magma objects in the category Mag. These are called auto magma objects. There's a more direct definition: an auto magma object is a set
X
together with a pair of 2-place operations
f
,
g
:
X
×
X
→
X
satisfying
g
(
f
(
x
,
y
)
,
f
(
x
′
,
y
′
)
)
=
f
(
g
(
x
,
x
′
)
,
g
(
y
,
y
′
)
)
. A medial magma is the special case where these operations are equal.
