Show simple item record Menni, Matías 2018-08-24T19:15:54Z 2017-11
dc.identifier.citation Menni, Matías; The construction of \pi_0 in Axiomatic Cohesion; De Gruyter; Tbilisi Mathematical Journal; 10; 3; 11-2017; 183-207
dc.identifier.issn 1512-0139
dc.description.abstract We study a construction suggested by Lawvere to rationalize, within a generalization of Axiomatic Cohesion, the classical construction of 0 as the image of a natural map to a product of discrete spaces. A particular case of this construction produces, out of a local and hyperconnected geometric morphism p : E ! S, an idempotent monad pi_0 : E ightarrow E such that, for every X in E, pi_0 X = 1 if and only if (p^* Omega)^! : (p^* Omega)^1 ightarrow (p^* Omega)^X is an isomorphism. For instance, if E is the topological topos (over S = Set), the pi_0-algebras coincide with the totally separated (sequential) spaces. To illustrate the connection with classical topology we show that the pi_0-algebras in the category of compactly generated Hausdorff spaces are exactly the totally separated ones. Also, in order to relate the construction above with the axioms for Cohesion we prove that, for a local and hyperconnected p : E ightarrow S, p is pre-cohesive if and only if p^* : S ightarrow Eis cartesian closed. In this case, p_! = p_* pi_0 : E ightarrow S and the category of pi_0-algebras coincides with the subcategory p^* : S ightarrow E.
dc.format application/pdf
dc.language.iso eng
dc.publisher De Gruyter
dc.rights info:eu-repo/semantics/openAccess
dc.subject Axiomatic Cohesion
dc.subject Topology
dc.subject.classification Matemática Pura
dc.subject.classification Matemáticas
dc.subject.classification CIENCIAS NATURALES Y EXACTAS
dc.title The construction of \pi_0 in Axiomatic Cohesion
dc.type info:eu-repo/semantics/article
dc.type info:ar-repo/semantics/artículo
dc.type info:eu-repo/semantics/publishedVersion 2018-08-24T13:36:32Z
dc.journal.volume 10
dc.journal.number 3
dc.journal.pagination 183-207
dc.journal.pais Polonia
dc.journal.ciudad Varsovia
dc.description.fil Fil: Menni, Matías. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata; Argentina
dc.journal.title Tbilisi Mathematical Journal
dc.relation.alternativeid info:eu-repo/semantics/altIdentifier/doi/
dc.relation.alternativeid info:eu-repo/semantics/altIdentifier/url/
dc.conicet.fuente individual

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info:eu-repo/semantics/openAccess Excepto donde se diga explícitamente, este item se publica bajo la siguiente descripción: Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Unported (CC BY-NC-SA 2.5)