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The Michael completion of a topos spread by Marta Bunge; Jonathon Funk; Mamuka Jibladze; Thomas Streicher is a Mathematics article available to read on EtoBox.

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We continue the investigation of the extension into the topos realm of the concepts introduced by Fox (Cahiers Top. et Gà eometrie Di . Catà egoriques 36 (1995) 53) and Michael (Indag. Math. 25 (1963) 629) in connection with topological singular coverings. In particular, we construct an analog of the Michael completion of a spread and compare it with the analog of the Fox completion obtained earlier by the ÿrst two named authors (J. Appl. Algebra 113 (1996) 1). Two ingredients are present in our analysis of geometric morphisms ' : F → E between toposes bounded over a base topos S. The ÿrst is the nature of the domain of ', which need only be assumed to be a "deÿnable dominance" over S, a condition that is trivially satisÿed if S is a Boolean topos. The Heyting algebras arising from the object S of truth values in the base topos play a special role in that they classify the deÿnable monomorphisms in those toposes. The geometric morphisms F → F over E which preserve these Heyting algebras (and that are not typically complete) are said to be strongly pure. The second is the nature of ' itself, which is assumed to be some kind of a spread. Applied to a spread, the (strongly pure, weakl

Who reads The Michael completion of a topos spread?

Author

Marta Bunge; Jonathon Funk; Mamuka Jibladze; Thomas Streicher

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0022-4049)

Published

2002

Language

EN

Field

Mathematics (Physical Sciences)