Set-theoretic Issues
In general, given a category C and some class w of morphisms in the category, there is some question as to whether it is possible to form a localization w-1 C by inverting all the morphisms in w. The typical procedure for constructing the localization might result in a pair of objects with a proper class of morphisms between them. Avoiding such set-theoretic issues is one of the initial reasons for the development of the theory of model categories.
Read more about this topic: Localization Of A Category
Famous quotes containing the word issues:
“I can never bring you to realize the importance of sleeves, the suggestiveness of thumb-nails, or the great issues that may hang from a boot-lace.”
—Sir Arthur Conan Doyle (18591930)