Last Updated
：2025/12/04
full functor
Noun
Japanese Meaning
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。
（ plural ）
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(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.
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full functor
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.
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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.
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