最終更新日：2022/12/23
例文
An
inverse
limit
has
“natural
projections”
which
are
restrictions
of
the
projections
of
the
Cartesian
product
(to
a
domain
which
is
the
inverse
limit).
The
reason
why
the
projections
are
described
as
“natural”
would
be
the
following:
besides
the
functor
from
an
index
poset
to
the
inverse
system,
there
is
another
functor
from
the
same
index
poset
to
the
inverse
limit
of
that
system,
this
functor
being
a
constant
functor.
Then
there
is
a
natural
transformation
from
the
constant
functor
to
the
inverse
limit’s
functor:
the
components
of
such
natural
transformation
are
the
said
“natural
projections”.
復習用の問題
An inverse limit has “natural projections” which are restrictions of the projections of the Cartesian product (to a domain which is the inverse limit). The reason why the projections are described as “natural” would be the following: besides the functor from an index poset to the inverse system, there is another functor from the same index poset to the inverse limit of that system, this functor being a constant functor. Then there is a natural transformation from the constant functor to the inverse limit’s functor: the components of such natural transformation are the said “natural projections”.
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