منابع مشابه
Being Van Kampen is a universal property
Colimits that satisfy the Van Kampen condition have interesting exactness properties. We show that the elementary presentation of the Van Kampen condition is actually a characterisation of a universal property in the associated bicategory of spans. The main theorem states that Van Kampen cocones are precisely those diagrams in a category that induce bicolimit diagrams in its associated bicatego...
متن کاملVan Kampen theorems for toposes
In this paper we introduce the notion of an extensive 2-category, to be thought of as a “2-category of generalized spaces”. We consider an extensive 2-category K equipped with a binary-product-preserving pseudofunctor C : K op → CAT, which we think of as specifying the “coverings” of our generalized spaces. We prove, in this context, a van Kampen theorem which generalizes and refines one of Bro...
متن کاملA Generalized Van Kampen-flores Theorem
The «-skeleton of a (2« + 2)-simplex does not embed in R " . This well-known result is due (independently) to van Kampen, 1932, and Flores, 1933, who proved the case p = 2 of the following: Theorem. Let p be a prime, and let s and I be positive integers such that l(P 1) < P{s 1). Then, for any continuous map f from a (ps + p 2)dimensional simplex into R , there must exist p points {xx, ... , x ...
متن کاملVan Kampen diagrams are bicolimits in Span
In adhesive categories, pushouts along monomorphisms are Van Kampen (vk) squares, a special case of a more general notion called vk-diagram. Other examples of vk-diagrams include coproducts in extensive categories and strict initial objects. Extensive and adhesive categories characterise useful exactness properties of, respectively, coproducts and pushouts along monos and have found several app...
متن کاملThe Seifert–van Kampen Theorem in Homotopy
Homotopy type theory is a recent research area connecting type theory with homotopy theory by interpreting types as spaces. In particular, one can prove and mechanize type-theoretic analogues of homotopy-theoretic theorems, yielding “synthetic homotopy theory”. Here we consider the Seifert–van Kampen theorem, which characterizes the loop structure of spaces obtained by gluing. This is useful in...
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ژورنال
عنوان ژورنال: Logical Methods in Computer Science
سال: 2011
ISSN: 1860-5974
DOI: 10.2168/lmcs-7(1:14)2011