Exponentials in a Cartesian Closed Category Which Contains all Algebraic Domains

Xi, Xiaoyong; Li, Yongming

doi:10.1007/s10485-014-9378-3

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Lemma 42 Suppose That P Is ω-Algebraic (That Is It Has a C1

Introduction1

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2015

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“…The proof is completed. Lemma 4.4 [6] If a category C is a Cartesian closed full subcategory of ALG with P = K(P ) for each P ∈ Ob(C), then C is a full subcategory of FIN. …”

Section: Lemma 42 Suppose That P Is ω-Algebraic (That Is It Has a Cmentioning

confidence: 99%

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Cartesian Closed Subcategories of CON T ≪ ∗ $CONT_{\ll }^{{\kern 8pt}\ast }$

Zhi-jun

2015

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Let CONT be the category of continuous domains and Scott continuous mappings that preserve the way-below relation on domains. Let ω-ALG be the full subcategory of CONT consisting of all countably based algebraic domains, and FIN be the category of finite posets and monotone mappings. The main result proved in this paper is that FIN is the largest Cartesian closed full subcategory of ω-ALG . On the other hand, it is shown that the algebraic L-domains form a Cartesian closed full subcategory of ALG .

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“…The proof is completed. Lemma 4.4 [6] If a category C is a Cartesian closed full subcategory of ALG with P = K(P ) for each P ∈ Ob(C), then C is a full subcategory of FIN. …”

Section: Lemma 42 Suppose That P Is ω-Algebraic (That Is It Has a Cmentioning

confidence: 99%

“…Additionally, a question that whether exponentials in ALG (the full subcategory of CONT consisting of all algebraic domains) are the same as exponentials in CONT was posed by him. Recently, the question was partially solved by Xi and Li [6].…”

Section: Introductionmentioning

confidence: 99%