A collection of morphisms in a category whose codomain is a certain fixed object of that category, which collection is closed under precomposition by any morphism in the category.
From Middle English sive, syfe, from Old English sife, sibi, from Proto-West Germanic *sibi ("sieve"), from Proto-Indo-European *seyp-, *seyb-. Akin to German Sieb, Dutch zeef, Proto-Slavic *sito (Russian си́то, сев, се́ять).
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