English Dictionary

faithful functor

名詞

(category theory) A functor which maps morphisms from its source to its target category in such a way that the restriction of that mapping to any source hom-set is injective into the corresponding target hom-set.

日本語の意味

カテゴリ理論における忠実な関手。すなわち、始源となるカテゴリの各ホム集合における射の写像が、その対応する対象のホム集合内で単射（すなわち異なる射が異なる像に写る）となるように定義される関手を指す。

A faithful functor can distinguish non-equal morphisms by mapping them to distinct morphisms in the target category.

各ホム集合に対して単射となる函手は、異なる射を標的圏の異なる射に写すことで区別できる。

意味（1）

(category theory) A functor which maps morphisms from its source to its target category in such a way that the restriction of that mapping to any source hom-set is injective into the corresponding target hom-set.

faithful functors （ plural ）