Relevant bibliographies by topics / Filtered colimits

Academic literature on the topic 'Filtered colimits'

Author: Grafiati
Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Filtered colimits"

1

Higginbotham, Logan, and Kevin Sinclair. "Asymptotic filtered colimits." Topology and its Applications 270 (February 2020): 106944. http://dx.doi.org/10.1016/j.topol.2019.106944.

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2

Hovey, Mark. "Morava $E$-theory of filtered colimits." Transactions of the American Mathematical Society 360, no. 01 (January 1, 2008): 369–83. http://dx.doi.org/10.1090/s0002-9947-07-04298-5.

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3

van Oosten, Jaap. "Filtered colimits in the effective topos." Journal of Pure and Applied Algebra 205, no. 2 (May 2006): 446–51. http://dx.doi.org/10.1016/j.jpaa.2005.07.001.

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4

Lack, Stephen, and Giacomo Tendas. "Flat vs. filtered colimits in the enriched context." Advances in Mathematics 404 (August 2022): 108381. http://dx.doi.org/10.1016/j.aim.2022.108381.

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5

Borceux, Francis, and Carmen Quinteriro. "Enriched accessible categories." Bulletin of the Australian Mathematical Society 54, no. 3 (December 1996): 489–501. http://dx.doi.org/10.1017/s0004972700021900.

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We consider category theory enriched in a locally finitely presentable symmetric monoidal closed category ν. We define the ν-filtered colimits as those colimits weighted by a ν-flat presheaf and consider the corresponding notion of ν-accessible category. We prove that ν-accessible categories coincide with the categories of ν-flat presheaves and also with the categories of ν-points of the categories of ν-presheaves. Moreover, the ν-locally finitely presentable categories are exactly the ν-cocomplete finitely accessible ones. To prove this last result, we show that the Cauchy completion of a small ν-category Cis equivalent to the category of ν-finitely presentable ν-flat presheaves on C.
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6

Hu, Hongde. "Flat functors and free exact categories." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 60, no. 2 (April 1996): 143–56. http://dx.doi.org/10.1017/s1446788700037575.

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AbstractLet C be a small category with weak finite limits, and let Flat(C) be the category of flat functors from C to the category of small sets. We prove that the free exact completion of C is the category of set-valued functors of Flat (C) which preserve small products and filtered colimits. In case C has finite limits, this gives A. Carboni and R. C. Magno's result on the free exact completion of a small category with finite limits.
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7

Benson, Dave, Srikanth B. Iyengar, and Henning Krause. "Module categories for group algebras over commutative rings." Journal of K-Theory 11, no. 2 (March 6, 2013): 297–329. http://dx.doi.org/10.1017/is013001031jkt214.

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AbstractWe develop a suitable version of the stable module category of a finite group G over an arbitrary commutative ring k. The purpose of the construction is to produce a compactly generated triangulated category whose compact objects are the finitely presented kG-modules. The main idea is to form a localisation of the usual version of the stable module category with respect to the filtered colimits of weakly injective modules. There is also an analogous version of the homotopy category of weakly injective kG-modules and a recollement relating the stable category, the homotopy category, and the derived category of kG-modules.
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8

van Oosten, Jaap. "Erratum to “Filtered colimits in the effective topos” [Journal of Pure and Applied Algebra 205 (2006) 446–451]." Journal of Pure and Applied Algebra 206, no. 3 (August 2006): 370. http://dx.doi.org/10.1016/j.jpaa.2006.03.014.

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9

Beke, Tibor. "Theories of presheaf type." Journal of Symbolic Logic 69, no. 3 (September 2004): 923–34. http://dx.doi.org/10.2178/jsl/1096901776.

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Let us say that a geometric theory T is of presheaf type if its classifying topos is (equivalent to) a presheaf topos. (We adhere to the convention that geometric logic allows arbitrary disjunctions, while coherent logic means geometric and finitary.) Write Mod(T) for the category of Set-models and homomorphisms of T. The next proposition is well known; see, for example, MacLane–Moerdijk [13], pp. 381-386, and the textbook of Adámek–Rosický [1] for additional information:Proposition 0.1. For a category , the following properties are equivalent:(i) is a finitely accessible category in the sense of Makkai–Paré [14], i.e., it has filtered colimits and a small dense subcategory of finitely presentable objectsii) is equivalent to Pts, the category of points of some presheaf topos(iii) is equivalent to the free filtered cocompletion (also known as Ind-) of a small category .(iv) is equivalent to Mod(T) for some geometric theory of presheaf type.Moreover, if these are satisfied for a given , then the —in any of (i), (ii) and (iii)—can be taken to be the full subcategory of consisting of finitely presentable objects. (There may be inequivalent choices of , as it is in general only determined up to idempotent completion; this will not concern us.)This seems to completely solve the problem of identifying when T is of presheaf type: check whether Mod(T) is finitely accessible and if so, recover the presheaf topos as Set-functors on the full subcategory of finitely presentable models. There is a subtlety here, however, as pointed out (probably for the first time) by Johnstone [10].
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10

Schmitt, Vincent. "Completions of Non-Symmetric Metric Spaces Via Enriched Categories." gmj 16, no. 1 (March 2009): 157–82. http://dx.doi.org/10.1515/gmj.2009.157.

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Abstract It is known from [Lawvere, Repr. Theory Appl. Categ. 1: 1–37 2002] that nonsymmetric metric spaces correspond to enrichments over the monoidal closed category [0, ∞]. We use enriched category theory and in particular a generic notion of flatness to describe various completions for these spaces. We characterise the weights of colimits commuting in the base category [0, ∞] with the conical terminal object and cotensors. Those can be interpreted in metric terms as very general filters, which we call filters of type 1. This correspondence extends the one between minimal Cauchy filters and weights which are adjoint as modules. Translating elements of enriched category theory into the metric context, one obtains a notion of convergence for filters of type 1 with a related completeness notion for spaces, for which there exists a universal completion. Another smaller class of flat presheaves is also considered both in the context of both metric spaces and preorders. (The latter being enrichments over the monoidal closed category 2.) The corresponding completion for preorders is the so-called dcpo completion.
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