English Dictionary

full 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 surjective into the corresponding target hom-set.

日本語の意味

圏論において、ソースの圏からターゲットの圏へ射を写す際、各Hom集合（射集合）上での写像が全射（surjective）となるような関手のこと。つまり、全ての対象の射に対して、その像が対応するターゲットの射集合を網羅する関手。

Because a full functor sends each hom-set in the source onto the corresponding hom-set in the target, it often allows properties of morphisms to be studied entirely within the image category.

各ホム集合への写像が対応するホム集合へ全射になる函手は、像の圏だけで射の性質を研究できることが多い。

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 surjective into the corresponding target hom-set.

full functors （ plural ）