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Baer criterion in locally presentable categories [PDF]
Categories and General Algebraic Structures with ApplicationsIn this paper, some Baer type criteria are considered for locally presentable categories. Recalling the notion of the classical Baer criterion for injectivity, it is shown that a locally presentable category which has enough injectives and coproduct ...
Mojgan Mahmoudi, Alireza Mehdizadeh
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Homotopy locally presentable enriched categories
Theory and Applications of Categories, 2015 We develop a homotopy theory of categories enriched in a monoidal model category V. In particular, we deal with homotopy weighted limits and colimits, and homotopy local presentability.
Lack, Stephen, Rosicky, Jiri
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Six model categories for directed homotopy [PDF]
Categories and General Algebraic Structures with Applications, 2021 We construct a q-model structure, an h-model structure and an m-model structure on multipointed $d$-spaces and on flows. The two q-model structures are combinatorial and left determined and they coincide with the combinatorial model structures already ...
Philippe Gaucher
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An enriched view on the extended finitary monad--Lawvere theory correspondence [PDF]
Logical Methods in Computer Science, 2018 We give a new account of the correspondence, first established by Nishizawa--Power, between finitary monads and Lawvere theories over an arbitrary locally finitely presentable base.
Richard Garner, John Power
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Derived, coderived, and contraderived categories of locally presentable abelian categories [PDF]
Journal of Pure and Applied Algebra, 2022 LaTeX 2e with xy-pic; 50 pages, 5 commutative diagrams; v.2: Remarks 6.4 and 9.2 inserted, Introduction expanded, many references added; v.3: several misprints ...
Positselski, L. (Leonid) +1 more
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On Injectivity in Locally Presentable Categories [PDF]
Transactions of the American Mathematical Society, 1993 Classes of objects injective w.r.t. specified morphisms are known to be closed under products and retracts. We prove the converse: a class of objects in a locally presentable category is an injectivity class iff it is closed under products and retracts. This result requires a certain large-cardinal principle.
Adámek, Jiří, Rosický, Jiří
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A generalization of Ohkawa's theorem [PDF]
, 2013 A theorem due to Ohkawa states that the collection of Bousfield equivalence classes of spectra is a set. We extend this result to arbitrary combinatorial model categories.Comment: 13 pages; consequences in motivic homotopy theory have been ...
Casacuberta, Carles +2 more
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Some results on locally finitely presentable categories [PDF]
Transactions of the American Mathematical Society, 1987 We prove that any full subcategory of a locally finitely presentable (l.f.p.) category having small limits and filtered colimits preserved by the inclusion functor is itself l.f.p. Here "full" may be weakened to "full with respect to isomorphisms." Further, we characterize those left exact functors I : C
Makkai, M., Pitts, A. M.
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Local Presentability of Certain Comma Categories
Applied Categorical Structures, 2019 It follows from standard results that if A and C are locally ^presentable categories and F:A^C is a ^-accessible functor, then the comma category IdC^F is locally ^-presentable. We show that, under the same hypotheses, F^IdC is also locally ^-presentable.
Andrew Polonsky, Patricia Johann
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Nearly locally presentable categories
Theory and Applications of Categories, 2018 We introduce a new class of categories generalizing locally presentable ones. The distinction does not manifest in the abelian case and, assuming Vopenka's principle, the same happens in the regular case. The category of complete partial orders is the natural example of a nearly locally finitely presentable category which is not locally presentable.
Positselski, L., Rosicky, J.
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