Last Updated
：2025/12/05
direct system
Noun
Japanese Meaning
（代数学において）有向順序集合を定義域とする共変関手の像として得られる、具体的な圏内の代数構造（例：加群）とそれらの間の射（例：加群準同型）からなる小さな圏を指す。
（ plural ）
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(algebra) A set of algebraic structures (which are part of a concrete category; e.g., modules) and a set of morphisms between them (e.g., module homomorphisms) which all together form a small category which is the image of a covariant functor whose domain is a directed poset.
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direct system
To compute the colimit, the algebraist assembled a direct system of modules with compatible homomorphisms.
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To compute the colimit, the algebraist assembled a direct system of modules with compatible homomorphisms.
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