منابع مشابه
Quasitoposes, Quasiadhesive Categories and Artin Glueing
Adhesive categories are a class of categories in which pushouts along monos are well-behaved with respect to pullbacks. Recently it has been shown that any topos is adhesive. Many examples of interest to computer scientists are not adhesive, a fact which motivated the introduction of quasiadhesive categories. We show that several of these examples arise via a glueing construction which yields q...
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We prove how any (elementary) topos may be reconstructed from the data of two complemented subtoposes together with a pair of left exact “glueing functors”. This generalizes the classical glueing theorem for toposes, which deals with the special case of an open subtopos and its closed complement. Our glueing analysis applies in a particularly simple form to a locally closed subtopos and its com...
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One of the important tools for working with the classifying toposes is Diaconescu's theorem, describing geometric morphisms to the topos of presheaves on a small category C in terms of at functors on C. In 4], this theorem is generalized from discrete categories to topological categories, with the additional requirement that the map assigning to an arrow its source is etale (a local homeomorphi...
متن کاملArtin Approximation
In 1968, M. Artin proved that any formal power series solution of a system of analytic equations may be approximated by convergent power series solutions. Motivated by this result and a similar result of Płoski, he conjectured that this remains true when we replace the ring of convergent power series by a more general ring. This paper presents the state of the art on this problem, aimed at non-...
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Emil Artin was born on March 3, 1898 in Vienna, as the son of an art dealer and an opera singer, and he died on December 20, 1962 in Hamburg. He was one of the founding fathers of modern algebra. Van der Waerden acknowledged his debt to Artin and to Emmy Noether (1882–1935) on the title page of his Moderne Algebra (1930–31), which indeed was originally conceived to be jointly written with Artin...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1974
ISSN: 0022-4049
DOI: 10.1016/0022-4049(74)90014-0