Completeness of cocompletions

Karazeris, Panagis; Rosický, Jiřı́; Velebil, Jiřı́

doi:10.1016/j.jpaa.2004.08.019

Cited by 5 publications

(3 citation statements)

References 11 publications

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“…Thus µ-presentable objects in P(A) are µ-presentable in P(A 0 ). Since the latter objects are closed under finite limits (see [21] 4.9), µ-presentable objects in P(A) are closed under finite conical limits. It remains to show that they are closed under cotensors with finitely presentable simplicial sets.…”

Section: Class-combinatorial Model Categoriesmentioning

confidence: 99%

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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Section: Class-combinatorial Model Categoriesmentioning

confidence: 99%

Generalized parton distributions of the photon for nonzero skewness

Mukherjee

Nair

2012

Physics Letters B

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“…For the first part of this section we suppose that V = Set, leading to Theorem 5.1. The latter should be attributed to Freyd, although it may not have been written down by him in exactly this form; it is a special case of [9,Theorem 4.8]. We include it as a warm-up for the more general case where the underlying category V 0 of V is a presheaf category.…”

Section: This Provides An Alternative Proof Ofmentioning

confidence: 99%

“…Rosický also characterized, in the case V = Set, when PK is cartesian closed; see Example 7.4 below. In a slightly different direction, the existence of limits in free completions under some class of colimits was studied in [9].…”

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confidence: 99%

Limits of small functors

Day

Lack

2007

Journal of Pure and Applied Algebra

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For a small category K enriched over a suitable monoidal category V, the free completion of K under colimits is the presheaf category [K*,V]. If K is large, its free completion under colimits is the V-category PK of small presheaves on K, where a presheaf is small if it is a left Kan extension of some presheaf with small domain. We study the existence of limits and of monoidal closed structures on PK.Comment: 17 page

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Flatness, weakly lex colimits, and free exact completions

Tendas

2023

Annali di Matematica

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We capture in the context of lex colimits, introduced by Garner and Lack, the universal property of the free regular and Barr-exact completions of a weakly lex category. This is done by introducing a notion of flatness for functors $$F:{{\mathcal {C}}}\rightarrow {{\mathcal {E}}}$$ F : C → E with lex codomain, and using this to describe the universal property of free $$\Phi $$ Φ -exact completions in the absence of finite limits, for any given class $$\Phi $$ Φ of lex weights. In particular, we shall give necessary and sufficient conditions for the existence of free lextensive and free pretopos completions in the non-lex world, and prove that the ultraproducts, in the categories of models of such completions, satisfy an universal property.

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Completeness of cocompletions

Cited by 5 publications

References 11 publications

Generalized parton distributions of the photon for nonzero skewness

Generalized parton distributions of the photon for nonzero skewness

Limits of small functors

Flatness, weakly lex colimits, and free exact completions

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