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pro vyhledávání: '"Janelidze, George"'
We characterize effective descent morphisms of what we call filtered preorders, and apply these results to slightly improve a known result, due to the first author and F. Lucatelli Nunes, on the effective descent morphisms in lax comma categories of
Externí odkaz:
http://arxiv.org/abs/2312.14315
Autor:
Janelidze, George, Sobral, Manuela
By a closure space we will mean a pair $(A,\mathcal{C})$, in which $A$ is a set and $\mathcal{C}$ a set of subsets of $A$ closed under arbitrary intersections. The purpose of this paper is to initiate a development of descent theory of closure spaces
Externí odkaz:
http://arxiv.org/abs/2310.16636
Autor:
Janelidze, George
The purpose of this paper is to initiate a development of a new non-pointed counterpart of semi-abelian categorical algebra. We are making, however, only the first step in it by giving equivalent definitions of what we call ideally exact categories,
Externí odkaz:
http://arxiv.org/abs/2308.06574
Autor:
Janelidze, George, Sobral, Manuela
For a commutative semiring S, by an S-algebra we mean a commutative semiring A equipped with a homomorphism from S to A. We show that the subvariety of S-algebras determined by the identities 1+2x=1 and x^2=x is closed under non-empty colimits. The (
Externí odkaz:
http://arxiv.org/abs/2307.04383
Autor:
Janelidze, George
A central extension is a regular epimorphism in a Barr exact category $\mathscr{C}$ satisfying suitable conditions involving a given Birkhoff subcategory of $\mathscr{C}$ (joint work with G. M. Kelly, 1994). In this paper we take $\mathscr{C}$ to be
Externí odkaz:
http://arxiv.org/abs/2206.02744
The main purpose of this paper is a wide generalization of one of the results abstract algebraic geometry begins with, namely of the fact that the prime spectrum $\mathrm{Spec}(R)$ of a unital commutative ring $R$ is always a spectral (=coherent) top
Externí odkaz:
http://arxiv.org/abs/2104.09840
Publikováno v:
Rendiconti del Seminario Matematico dell'Universit\`a di Padova, Vol.144, 2020, 13-25
The paper is devoted to a kind of `very non-abelian' spectral categories. Under strong conditions on a category $\mathcal{X}$, we prove, among other things, that, for a given faithful localization $\mathcal{C}\to\mathcal{X}$, we have canonical equiva
Externí odkaz:
http://arxiv.org/abs/2002.08234
We generalize the van Kampen theorem for unions of non-connected spaces, due to R. Brown and A. R. Salleh, to the context where families of subspaces of a space B are replaced by a locally sectionable map to B.
Comment: version 3, expanded proof
Comment: version 3, expanded proof
Externí odkaz:
http://arxiv.org/abs/1910.11620
Publikováno v:
Comment. Math. Univ. Carolin. 60, 4 (2019) 509-527
We develop a theory of split extensions of unitary magmas, which includes defining such extensions and describing them via suitably defined semidirect product, yielding an equivalence between the categories of split extensions and of (suitably define
Externí odkaz:
http://arxiv.org/abs/1906.02310
Publikováno v:
In: Facchini A., Fontana M., Geroldinger A., Olberding B. (eds) Advances in Rings, Modules and Factorizations. Rings and Factorizations 2018. Springer Proceedings in Mathematics & Statistics, vol 321. Springer (2020) 135-152
For a category $\mathcal{C}$ with finite limits and a class $\mathcal{S}$ of monomorphisms in $\mathcal{C}$ that is pullback stable, contains all isomorphisms, is closed under composition, and has the strong left cancellation property, we use pullbac
Externí odkaz:
http://arxiv.org/abs/1903.10034