Categories of imaginaries for definable additive categories
نویسنده
چکیده
An additive category is definable if it is equivalent to a definable subcategory of a module category Mod-R, meaning a full subcategory which is closed under direct products, direct limits (= directed colimits) and pure subobjects. Such a category D has associated to it a canonical model theory for its objects in the sense that each object D ∈ D becomes a structure for the associated language; as such, D is a model of the associated theory and D is the category of models for that theory. The model theory, moreover, is essentially just like the model theory of modules over a ring, hence very amenable, in particular the theory of D (the common theory of the objects of D) has pp-elimination of quantifiers. The associated category of pp-imaginaries is abelian and every
منابع مشابه
Definable Additive Categories
This is essentially the talk I gave on definable additive categories; I define these categories, say where they came from, describe some of what is around them and then point out the 2-category which
متن کاملAbelian categories and definable additive categories
2 The category of small abelian categories and exact functors 4 2.1 Categorical properties of ABEX . . . . . . . . . . . . . . . . . . . 5 2.2 Pullbacks in ABEX . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 ABEX is finitely accessible . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Abelian categories as schemes . . . . . . . . . . . . . . . . . . . . 16 2.4.1 The functor of point...
متن کاملA pathological o-minimal quotient
We give an example of a definable quotient in an o-minimal structure which cannot be eliminated over any set of parameters, giving a negative answer to a question of Eleftheriou, Peterzil, and Ramakrishnan. Equivalently, there is an o-minimal structure M whose elementary diagram does not eliminate imaginaries. We also give a positive answer to a related question, showing that any imaginary in a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012