Limits of small functors

Day, Brian J.; Lack, Stephen

doi:10.1016/j.jpaa.2006.10.019

Cited by 50 publications

(90 citation statements)

References 11 publications

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“…. (see the proof of [12], 5.2). Thus we have to show that µ-presentable objects in P(A) are closed under cotensors with ∆ n 's.…”

Section: Class-combinatorial Model Categoriesmentioning

confidence: 85%

“…Given a simplicial category A, by abuse of notation, P(A) will denote the category of small simplicial presheaves on A. The objects are functors A op → SSet which are small weighted colimits of simplicial representable functors (see [12]). In [10], we used this notation for small presheaves on a category A but it will cause any misunderstanding.…”

Section: Class-combinatorial Model Categoriesmentioning

confidence: 99%

“…In [10], we used this notation for small presheaves on a category A but it will cause any misunderstanding. The simplicial category P(A) is complete provided that A is complete (see [12]); completeness is meant in the enriched sense (see, e.g., [4] or [22]). …”

Section: Class-combinatorial Model Categoriesmentioning

confidence: 99%

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Generalized parton distributions of the photon for nonzero skewness

Mukherjee

Nair

2012

Physics Letters B

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Abstract. We extend the framework of combinatorial model categories, so that the category of small presheaves over large indexing categories and ind-categories would be embraced by the new machinery called class-combinatorial model categories.The definition of the new class of model categories is based on the corresponding extension of the theory of locally presentable and accessible categories developed in the companion paper [10], where we introduced the concepts of locally class-presentable and class-accessible categories.In this work we prove that the category of weak equivalences of a nice class-combinatorial model category is class-accessible. Our extension of J. Smith localization theorem depends on the verification of a cosolution-set condition. The deepest result is that the (left Bousfield) localization of a class-combinatorial model category with respect to a strongly class-accessible localization functor is class-combinatorial again.

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“…. (see the proof of [12], 5.2). Thus we have to show that µ-presentable objects in P(A) are closed under cotensors with ∆ n 's.…”

Section: Class-combinatorial Model Categoriesmentioning

confidence: 85%

Section: Class-combinatorial Model Categoriesmentioning

confidence: 99%

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Generalized parton distributions of the photon for nonzero skewness

Mukherjee

Nair

2012

Physics Letters B

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“…This extends to a pseudomonad on V -Cat, whose unit has components the Yoneda embedding y C : C Ñ PC, and whose multiplication we denote by m P . A number of properties of PC, in particular its completeness, are studied in [6].…”

Section: Example: Completion Of V -Categories Under a Class Of Colimitsmentioning

confidence: 99%

Lax orthogonal factorisation systems

Clementino

Franco

2016

Advances in Mathematics

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Abstract. This paper introduces lax orthogonal algebraic weak factorisation systems on 2-categories and describes a method of constructing them. This method rests in the notion of simple 2-monad, that is a generalisation of the simple reflections studied by Cassidy, Hébert and Kelly. Each simple 2-monad on a finitely complete 2-category gives rise to a lax orthogonal algebraic weak factorisation system, and an example of a simple 2-monad is given by completion under a class of colimits. The notions of kz lifting operation, lax natural lifting operation and lax orthogonality between morphisms are studied.

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“…For enriched settings, our main reference is the work of B. Day and S. Lack [15]. Recently, several applications of small functors from spaces to spaces have appeared in homotopy theory [2], [10].…”

Section: Introductionmentioning

confidence: 99%

Duality and small functors

Biedermann

Chorny

2015

Algebr. Geom. Topol.

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Abstract. The homotopy theory of small functors is a useful tool for studying various questions in homotopy theory. In this paper, we develop the homotopy theory of small functors from spectra to spectra, and study its interplay with Spanier-Whitehead duality and enriched representability in the dual category of spectra.We note that Spanier-Whitehead duality functor D : Sp → Sp op factors through the category of small functors from spectra to spectra, and construct a new model structure on the category of small functors, which is Quillen equivalent to Sp op . In this new framework for the Spanier-Whitehead duality, Sp and Sp op are full subcategories of the category of small functors and dualization becomes just a fibrant replacement in our new model structure.

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Limits of small functors

Cited by 50 publications

References 11 publications

Generalized parton distributions of the photon for nonzero skewness

Generalized parton distributions of the photon for nonzero skewness

Lax orthogonal factorisation systems

Duality and small functors

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