Inverse hypersystems (CROSBI ID 178593)
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Podaci o odgovornosti
Uglešić, Nikica
engleski
Inverse hypersystems
The notion of a (generalized) inverse hypersystem in a category 𝒞, that generalizes the known notion of a generalized inverse system, is introduced via a functor of a cofinally small weakly cofiltered category to 𝒞. The appropriate morphisms are also defined such that they generalize the morphisms of generalized inverse systems. The corresponding category 𝑃𝑅𝑂-𝒞 is constructed such that 𝑝𝑟𝑜-𝒞 and 𝑃𝑟𝑜- 𝒞 are subcategories of it. In comparison to the relationship between 𝑝𝑟𝑜-𝒞 and 𝑃𝑟𝑜-𝒞, the essential benefit is that there exist inverse hypersystems which are not isomorphic to any generalized inverse system. The notion of a cofinite inverse hypersystem is also introduced, and it is proven that every generalized inverse hypersystem is isomorphic to a cofinite inverse hypersystem. At the end, it is shown by example how an inverse hypersystem could occur.
cofiltered category; generalized inverse system; inverse system; pro-category
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