Source Word
natural transformation
Noun
(category
theory)
A
morphism
between
a
pair
of
parallel
functors
such
that
if
each
object
of
the
shared
domain
category
subtends
a
correlated
arrow
—
called
a
component
—
in
the
shared
codomain
(which
arrow
represents
the
difference
between
applying
the
second
functor
and
the
first
functor
to
the
correlated
object)
then
each
arrow
of
the
shared
domain
subtends
a
commuting
square
—
called
a
naturality
square
—
between
two
components
(correlated
to
the
domain
and
codomain
of
the
arrow).
Japanese Meaning
圏論において、二つの平行な関手の間の射（自然変換）を意味する。具体的には、ある圏から二つの関手が与えられたとき、各対象に対して対応する射（成分）を割り当て、その対応が射に関して自然性条件、すなわち各射に対応する自然性正方形が可換になるという性質を持つ変換を指す。
Sense（1）
(category
theory)
A
morphism
between
a
pair
of
parallel
functors
such
that
if
each
object
of
the
shared
domain
category
subtends
a
correlated
arrow
—
called
a
component
—
in
the
shared
codomain
(which
arrow
represents
the
difference
between
applying
the
second
functor
and
the
first
functor
to
the
correlated
object)
then
each
arrow
of
the
shared
domain
subtends
a
commuting
square
—
called
a
naturality
square
—
between
two
components
(correlated
to
the
domain
and
codomain
of
the
arrow).
（ plural ）
