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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
core   +3 more sources

Baer criterion in locally presentable categories [PDF]

Categories and General Algebraic Structures with Applications
In 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
doaj   +2 more sources

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), Šťovíček, J.   +1 more
openaire   +4 more sources

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
openaire   +1 more source

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, Gutiérrez, Javier J., Rosický, Jirí   +2 more
core   +7 more sources

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.
openaire   +3 more sources

Localisations of locally presentable categories II

Journal of Pure and Applied Algebra, 1990
This is a continuation of Part I [ibid. 58, No.3, 227-233 (1989; Zbl 0677.18009)]. However, it does not deal with enriched categories; the authors content themselves to consider localizations E of categories \(A=Lex(C^{op},Set)\). They show how E arises as Lex Sh\({}_ J(C)\) for a Grothendieck topology on C.
Day, Brian, Street, Ross
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n-permutable locally finitely presentable categories

Theory and Applications of Categories, 2001
\(n\)-permutable locally finitely presentable categories are characterized in terms of properties of their finitely presentable objects. As a consequence, they get a similar characterization of regular Maltsev locally finitely presentable categories.
PEDICCHIO, MARIA CRISTINA, M. GRAN
openaire   +3 more sources