English Dictionary

well-pointed

形容詞

比較不可

(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.

日本語の意味

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。

A well-pointed topos has no zero object and ensures that any distinct pair of parallel morphisms can be distinguished by composing them with a global element of their domain.

終対象を持ち（トポスの場合は零対象が存在せず）、任意の異なる平行射がその定義域のグローバル要素との合成によって区別できる圏である。

意味（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.