Last Updated：2025/12/05
(category theory) Said of a category or topos: that it has a terminal object (or that it has no zero object, if it is a topos) and in which any distinct pair of parallel morphisms can be distinguished by their distinct compositions with a global element of their domain; i.e. any pair of parallel morphisms is distinct if and only if there is a global element in their domain that does not equalize them.
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well-pointed
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Source Word
well-pointed
Adjective
not-comparable
(category
theory)
Said
of
a
category
or
topos:
that
it
has
a
terminal
object
(or
that
it
has
no
zero
object,
if
it
is
a
topos)
and
in
which
any
distinct
pair
of
parallel
morphisms
can
be
distinguished
by
their
distinct
compositions
with
a
global
element
of
their
domain;
i.e.
any
pair
of
parallel
morphisms
is
distinct
if
and
only
if
there
is
a
global
element
in
their
domain
that
does
not
equalize
them.
Japanese Meaning
圏論において、「well-pointed」とは、ある圏またはトポスが終対象（またはトポスの場合には零対象を持たない）を有し、その定義域からのグローバル要素を用いた合成により、任意の異なる平行射が互いに区別できるという性質を指す。
Sense（1）
(category
theory)
Said
of
a
category
or
topos:
that
it
has
a
terminal
object
(or
that
it
has
no
zero
object,
if
it
is
a
topos)
and
in
which
any
distinct
pair
of
parallel
morphisms
can
be
distinguished
by
their
distinct
compositions
with
a
global
element
of
their
domain;
i.e.
any
pair
of
parallel
morphisms
is
distinct
if
and
only
if
there
is
a
global
element
in
their
domain
that
does
not
equalize
them.
