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- W2025831907 abstract "Let ACG be the category of cogroups in the category A of connected graded algebras over a fixed commutative ring R. We study the full subcategory ACGco consisting of objects whose underlying algebras are graded commutative, together with the full subcategory AcoCG consisting of cocommutative objects and the full subcategory ACGco consisting of objects whose underlying coalgebras are graded cocommutative. We establish categorical equivalences of these full subcategories with categories of simpler algebraic objects, and obtain the inclusion relation of the full subcategories. Since H⁎(ΩX;R) is a cogroup in A for a 1-connected co-H-group (under the assumption that R is a field), the algebraic results are applied to the theory of co-H-groups. We study when H⁎(ΩX;R) is in AcoCG or ACGco, and generalize a theorem of Kachi." @default.
- W2025831907 created "2016-06-24" @default.
- W2025831907 creator A5004911196 @default.
- W2025831907 date "2015-07-01" @default.
- W2025831907 modified "2023-09-30" @default.
- W2025831907 title "Commutativity and cocommutativity of cogroups in the category of connected graded algebras" @default.
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- W2025831907 doi "https://doi.org/10.1016/j.topol.2015.04.003" @default.
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