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Co-H-structures on equivariant Moore spaces

Martin Arkowitz, Marek Golasiński (1994)

Fundamenta Mathematicae

Let G be a finite group, 𝕆 G the category of canonical orbits of G and A : 𝕆 G 𝔸 b a contravariant functor to the category of abelian groups. We investigate the set of G-homotopy classes of comultiplications of a Moore G-space of type (A,n) where n ≥ 2 and prove that if such a Moore G-space X is a cogroup, then it has a unique comultiplication if dim X < 2n - 1. If dim X = 2n-1, then the set of comultiplications of X is in one-one correspondence with E x t n - 1 ( A , A A ) . Then the case G = p k leads to an example of infinitely...

Colimit-dense subcategories

Jiří Adámek, Andrew D. Brooke-Taylor, Tim Campion, Leonid Positselski, Jiří Rosický (2019)

Commentationes Mathematicae Universitatis Carolinae

Among cocomplete categories, the locally presentable ones can be defined as those with a strong generator consisting of presentable objects. Assuming Vopěnka’s Principle, we prove that a cocomplete category is locally presentable if and only if it has a colimit dense subcategory and a generator consisting of presentable objects. We further show that a 3 -element set is colimit-dense in 𝐒𝐞𝐭 op , and spaces of countable dimension are colimit-dense in 𝐕𝐞𝐜 op .

Compact corigid objects in triangulated categories and co-t-structures

David Pauksztello (2008)

Open Mathematics

In the work of Hoshino, Kato and Miyachi, [11], the authors look at t-structures induced by a compact object, C , of a triangulated category, 𝒯 , which is rigid in the sense of Iyama and Yoshino, [12]. Hoshino, Kato and Miyachi show that such an object yields a non-degenerate t-structure on 𝒯 whose heart is equivalent to Mod(End( C )op). Rigid objects in a triangulated category can the thought of as behaving like chain differential graded algebras (DGAs). Analogously, looking at objects which behave...

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