Zobrazeno 1 - 10
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pro vyhledávání: '"Adamek, Jiri"'
Autor:
Adamek, Jiri
Classical varieties were characterized by Lawvere as the categories with effective congruences and a varietal generator: an abstractly finite regular generator which is regularly projective (its hom-functor preserves regular epimorphisms). We charact
Externí odkaz:
http://arxiv.org/abs/2402.14662
Autor:
Adamek, Jiri
Following ideas of Lawvere and Linton we prove that classical varieties are precisely the exact categories with a varietal generator. This means a strong generator which is abstractly finite and regularly projective. An analogous characterization of
Externí odkaz:
http://arxiv.org/abs/2402.14557
Autor:
Adámek, Jirí, Sousa, Lurdes
Graduated locally finitely presentable categories are introduced, examples include categories of sets, vector spaces, posets, presheaves and Boolean algebras. A finitary functor between graduated locally finitely presentable categories is proved to b
Externí odkaz:
http://arxiv.org/abs/2311.14965
The Vietoris space of compact subsets of a given Hausdorff space yields an endofunctor $\mathscr V$ on the category of Hausdorff spaces. Vietoris polynomial endofunctors on that category are built from $\mathscr V$, the identity and constant functors
Externí odkaz:
http://arxiv.org/abs/2303.11071
Quillen's notion of small object and the Gabriel-Ulmer notion of finitely presentable or generated object are fundamental in homotopy theory and categorical algebra. Do these notions always lead to rather uninteresting classes of objects in categorie
Externí odkaz:
http://arxiv.org/abs/2302.00050
We characterize strongly finitary monads on categories $\mathsf{Pos}$, $\mathsf{CPO}$ and $\mathsf{DCPO}$ as precisely those preserving sifted colimits. Or, equivalently, enriched finitary monads preserving reflexive coinserters. We study sifted coli
Externí odkaz:
http://arxiv.org/abs/2301.05730
Quantitative algebras are algebras enriched in the category $\mathsf{Met}$ of metric spaces so that all operations are nonexpanding. Mardare, Plotkin and Panangaden introduced varieties (aka $1$-basic varieties) as classes of quantitative algebras pr
Externí odkaz:
http://arxiv.org/abs/2301.01034
Autor:
Adámek, Jiří, Rosický, Jiří
Publikováno v:
Alg. Univ. 84:9 (2023)
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 to a variety. This is quite analogous to Lawvere's classical character
Externí odkaz:
http://arxiv.org/abs/2110.06613
Publikováno v:
Proc. 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021), volume 211 of LIPIcs, pages 5:1-5:20
The Initial Algebra Theorem by Trnkov\'a et al.~states, under mild assumptions, that an endofunctor has an initial algebra provided it has a pre-fixed point. The proof crucially depends on transfinitely iterating the functor and in fact shows that, e
Externí odkaz:
http://arxiv.org/abs/2104.09837
Autor:
Adamek, Jiri
A number of categories is presented that are algebraically complete and cocomplete, i.e., every endofunctor has an initial algebra and a terminal coalgebra. For all finitary (and, more generally, all precontinuous) set functors the initial algebra an
Externí odkaz:
http://arxiv.org/abs/2102.06532