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dbr:Limit_and_colimit_of_presheaves
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dbr:Density_theorem_(category_theory)
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降下理論 (圏論) Density theorem (category theory)
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降下理論（こうかりろん）は、数学の一分野である圏論の定理であり、集合のすべての前層が標準的な方法で表現可能な前層の極限であると主張している。 In category theory, a branch of mathematics, the density theorem states that every presheaf of sets is a colimit of representable presheaves in a canonical way. For example, by definition, a simplicial set is a presheaf on the simplex category Δ and a representable simplicial set is exactly of the form (called the standard n-simplex) so the theorem says: for each simplicial set X, where the colim runs over an index category determined by X.
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In category theory, a branch of mathematics, the density theorem states that every presheaf of sets is a colimit of representable presheaves in a canonical way. For example, by definition, a simplicial set is a presheaf on the simplex category Δ and a representable simplicial set is exactly of the form (called the standard n-simplex) so the theorem says: for each simplicial set X, where the colim runs over an index category determined by X. 降下理論（こうかりろん）は、数学の一分野である圏論の定理であり、集合のすべての前層が標準的な方法で表現可能な前層の極限であると主張している。
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