Displaying similar documents to “Limits and colimits in certain categories of spaces of continuous functions”

Stable tubes in extriangulated categories

Li Wang, Jiaqun Wei, Haicheng Zhang (2022)

Czechoslovak Mathematical Journal

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Let 𝒳 be a semibrick in an extriangulated category. If 𝒳 is a τ -semibrick, then the Auslander-Reiten quiver Γ ( ( 𝒳 ) ) of the filtration subcategory ( 𝒳 ) generated by 𝒳 is 𝔸 . If 𝒳 = { X i } i = 1 t is a τ -cycle semibrick, then Γ ( ( 𝒳 ) ) is 𝔸 / τ 𝔸 t .

Cotorsion pairs in comma categories

Yuan Yuan, Jian He, Dejun Wu (2024)

Czechoslovak Mathematical Journal

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Let 𝒜 and be abelian categories with enough projective and injective objects, and T : 𝒜 a left exact additive functor. Then one has a comma category ( T ) . It is shown that if T : 𝒜 is 𝒳 -exact, then ( 𝒳 , 𝒳 ) is a (hereditary) cotorsion pair in 𝒜 and ( 𝒴 , 𝒴 ) ) is a (hereditary) cotorsion pair in if and only if 𝒳 𝒴 , 𝐡 ( 𝒳 , 𝒴 ) ) is a (hereditary) cotorsion pair in ( T ) and 𝒳 and 𝒴 are closed under extensions. Furthermore, we characterize when special preenveloping classes in abelian categories 𝒜 and can induce special preenveloping...

On category 𝒪 for cyclotomic rational Cherednik algebras

Iain G. Gordon, Ivan Losev (2014)

Journal of the European Mathematical Society

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We study equivalences for category 𝒪 p of the rational Cherednik algebras 𝐇 p of type G ( n ) = ( μ ) n 𝔖 n : a highest weight equivalence between 𝒪 p and 𝒪 σ ( p ) for σ 𝔖 and an action of 𝔖 on an explicit non-empty Zariski open set of parameters p ; a derived equivalence between 𝒪 p and 𝒪 p ' whenever p and p ' have integral difference; a highest weight equivalence between 𝒪 p and a parabolic category 𝒪 for the general linear group, under a non-rationality assumption on the parameter p . As a consequence, we confirm special cases...

On almost complex structures from classical linear connections

Jan Kurek, Włodzimierz M. Mikulski (2017)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Let f m be the category of m -dimensional manifolds and local diffeomorphisms and  let T be the tangent functor on f m . Let 𝒱 be the category of real vector spaces and linear maps and let 𝒱 m be the category of m -dimensional real vector spaces and linear isomorphisms. We characterize all regular covariant functors F : 𝒱 m 𝒱 admitting f m -natural operators J ˜ transforming classical linear connections on m -dimensional manifolds M into almost complex structures J ˜ ( ) on F ( T ) M = x M F ( T x M ) .

Hall algebras of two equivalent extriangulated categories

Shiquan Ruan, Li Wang, Haicheng Zhang (2024)

Czechoslovak Mathematical Journal

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For any positive integer n , let A n be a linearly oriented quiver of type A with n vertices. It is well-known that the quotient of an exact category by projective-injectives is an extriangulated category. We show that there exists an extriangulated equivalence between the extriangulated categories n + 1 and n , where n + 1 and n are the two extriangulated categories corresponding to the representation category of A n + 1 and the morphism category of projective representations of A n , respectively. As a...

On the structure of triangulated categories with finitely many indecomposables

Claire Amiot (2007)

Bulletin de la Société Mathématique de France

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We study the problem of classifying triangulated categories with finite-dimensional morphism spaces and finitely many indecomposables over an algebraically closed field k . We obtain a new proof of the following result due to Xiao and Zhu: the Auslander-Reiten quiver of such a category 𝒯 is of the form Δ / G where Δ is a disjoint union of simply-laced Dynkin diagrams and G a weakly admissible group of automorphisms of Δ . Then we prove that for ‘most’ groups G , the category 𝒯 is standard, ...

Σ s -products revisited

Reynaldo Rojas-Hernández (2015)

Commentationes Mathematicae Universitatis Carolinae

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We show that any Σ s -product of at most 𝔠 -many L Σ ( ω ) -spaces has the L Σ ( ω ) -property. This result generalizes some known results about L Σ ( ω ) -spaces. On the other hand, we prove that every Σ s -product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every Σ s -product of Collins-Roscoe spaces has the Collins-Roscoe property. These results generalize some known results about the Collins-Roscoe spaces and answer some questions due to Tkachuk [Lifting the Collins-Roscoe...

Higher-dimensional Auslander-Reiten sequences

Jiangsha Li, Jing He (2024)

Czechoslovak Mathematical Journal

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Zhou and Zhu have shown that if 𝒞 is an ( n + 2 ) -angulated category and 𝒳 is a cluster tilting subcategory of 𝒞 , then the quotient category 𝒞 / 𝒳 is an n -abelian category. We show that if 𝒞 has Auslander-Reiten ( n + 2 ) -angles, then 𝒞 / 𝒳 has Auslander-Reiten n -exact sequences.

The Roquette category of finite p -groups

Serge Bouc (2015)

Journal of the European Mathematical Society

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Let p be a prime number. This paper introduces the Roquette category p of finite p -groups, which is an additive tensor category containing all finite p -groups among its objects. In p , every finite p -group P admits a canonical direct summand P , called the edge of P . Moreover P splits uniquely as a direct sum of edges of Roquette p -groups, and the tensor structure of p can be described in terms of such edges. The main motivation for considering this category is that the additive functors...