51 citations · 273 across the 33 of their papers we have counts for
27 papers · 1 filter
Varieties of ordered algebras as categories
Jiří Adámek, Jiří Rosický
A variety is a category of ordered (finitary) algebras presented by inequations between terms. We characterize categories enriched over the category of posets which are equivalent…
Metric monads
JIří Rosický
We develop universal algebra over an enriched category and relate it to finitary enriched monads over . Using it, we deduce recent results about ordered un…
Are Banach spaces monadic?
Jiří Rosický
We will show that Banach spaces are monadic over complete metric spaces via the unit ball functor. For the forgetful functor, one should take complete pointed metric spaces.
Minimal accessible categories
Jiří Rosický
We give a purely category-theoretic proof of the result of Makkai and Paré saying that the category of linearly ordered sets and order preserving injective mappings is a…
Approximate injectivity and smallness in metric-enriched categories
Jiří Adámek, Jiří Rosický
Properties of categories enriched over the category of metric spaces are investigated and applied to a study of constructions known from that category and the category of Banach sp…
Cofibrant generation of pure monomorphisms
Michael Lieberman, Leonid Positselski, Jiri Rosicky +1
We show that pure monomorphisms are cofibrantly generated---generated from a set of morphisms by pushouts, transfinite composition, and retracts---in any locally finitely presentab…
Hilbert spaces and -algebras are not finitely concrete
Michael Lieberman, Jiří Rosický, Sebastien Vasey
We show that no faithful functor from the category of Hilbert spaces with linear isometries into the category of sets preserves directed colimits. Thus Hilbert spaces cannot form a…
Cellular categories and stable independence
Michael Lieberman, Jiří Rosický, Sebastien Vasey
We exhibit a bridge between the theory of cellular categories, used in algebraic topology and homological algebra, and the model-theoretic notion of stable independence. Roughly sp…
Nearly locally presentable categories
Leonid Positselski, Jiri Rosicky
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 happ…
On the uniqueness of cellular injectives
Jiří Rosický
A. Avilés and C. Brech proved a intriguing result about the existence and uniqueness of certain injective Boolean algebras or Banach spaces. Their result refines the standard exist…
Approximate injectivity
Jiri Rosicky, Walter Tholen
In a locally -presentable category, with a regular cardinal, classes of objects that are injective with respect to a family of morphisms whose domains and codomains are -…
Elementary equivalences and accessible functors
Tibor Beke, Jiri Rosicky
We introduce the notion of -equivalence and -embeddings of objects in suitable categories. This notion specializes to -equivalence and -elementary e…
Covers, envelopes, and cotorsion theories in locally presentable abelian categories and contramodule categories
Leonid Positselski, Jiri Rosicky
We prove general results about completeness of cotorsion theories and existence of covers and envelopes in locally presentable abelian categories, extending the well-established th…
On reflective subcategories of locally presentable categories
Jiri Adamek, Jiri Rosicky
Are all subcategories of locally finitely presentable categories that are closed under limits and -filtered colimits also locally presentable? For full subcategories the answer…
Accessible model categories
J. Rosicky
We prove that a weak factorization system on a locally presentable category is accessible if and only if it is small generated in the sense of R. Garner. Moreover, we discuss an an…
Cellular objects and Shelah's singular compactness theorem
Tibor Beke, Jiri Rosicky
The best-known version of Shelah's celebrated singular cardinal compactness theorem states that if the cardinality of an abelian group is singular, and all its subgroups of lesser…
Homotopy locally presentable enriched categories
Stephen Lack, Jiri Rosicky
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 presentabi…
Rigidification of algebras over essentially algebraic theories
J. Rosicky
Badzioch and Bergner proved a rigidification theorem saying that each homotopy simplicial algebra is weakly equivalent to a simplicial algebra. The question is whether this result…
Colimits of accessible categories
R. Pare, J. Rosicky
We show that any directed colimit of acessible categories and accessible full embeddings is accessible and, assuming the existence of arbitrarily large strongly compact cardinals,…
Locally class-presentable and class-accessible categories
Boris Chorny, Jiri Rosicky
We generalize the concepts of locally presentable and accessible categories. Our framework includes such categories as small presheaves over large categories and ind-categories. Th…
Definable orthogonality classes in accessible categories are small
Joan Bagaria, Carles Casacuberta, A. R. D. Mathias +1
We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopenka's p…
Enriched weakness
Stephen Lack, Jiri Rosicky
The basic notions of category theory, such as limit, adjunction, and orthogonality, all involve assertions of the existence and uniqueness of certain arrows. Weak notions arise whe…
Abstract elementary classes and accessible categories
Tibor Beke, Jiri Rosicky
We compare abstract elementary classes of Shelah with accessible categories having directed colimits.
Are all cofibrantly generated model categories combinatorial?
J. Rosicky
G. Raptis has recently proved that, assuming Vopěnka's principle, every cofibrantly generated model category is Quillen equivalent to a combinatorial one. His result remains true f…