منابع مشابه
Ring Completion of Rig Categories
In this paper we offer a solution to the long-standing problem of group completing within the context of rig categories (also known as bimonoidal categories). More precisely, given a rig category R we construct a natural additive group completion R̄ of R that retains the multiplicative structure, meaning that it remains a rig category. In other words, it has become a ring category. If we start w...
متن کاملUnivalent categories and the Rezk completion
We develop category theory within Univalent Foundations, which is a foundational system for mathematics based on a homotopical interpretation of dependent type theory. In this system, we propose a definition of " category " for which equality and equivalence of categories agree. Such categories satisfy a version of the Univalence Axiom, saying that the type of isomorphisms between any two objec...
متن کاملExact completion and representations in abelian categories
When the exact completion of a category with weak finite limits is a Mal’cev category, it is possible to combine the universal property of the exact completion and the universal property of the coequalizer completion. We use this fact to explain Freyd’s representation theorems in abelian and Frobenius categories. MSC 2000 : 18A35, 18B15, 18E10, 18G05.
متن کاملThe Relation between Ann-categories and Ring Categories
There are different categorizations of the definition of a ring such as Ann-category [6], ring category [2],... The main result of this paper is to prove that every axiom of the definition of a ring category, without the axiom x0 = y0, can be deduced from the axiomatics of an Ann-category.
متن کاملSymmetry and Cauchy Completion of Quantaloid-enriched Categories
We formulate an elementary condition on an involutive quantaloidQ under which there is a distributive law from the Cauchy completion monad over the symmetrisation comonad on the category of Q-enriched categories. For such quantaloids, which we call Cauchy-bilateral quantaloids, it follows that the Cauchy completion of any symmetric Q-enriched category is again symmetric. Examples include Lawver...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2013
ISSN: 1435-5345,0075-4102
DOI: 10.1515/crelle.2012.024