Extending Hrushovski's groupoid-cover correspondence using simplicial groupoids
نویسندگان
چکیده
Hrushovski's suggestion, given in ["Groupoids, imaginaries and internal covers," Turkish Journal of Mathematics , 2012], to capture the structure 1-analysable covers a theory T using simplicial groupoids definable is realized here. The ideas Haykazyan Moosa, found ["Functoriality uniformity groupoid-cover correspondence," Annals Pure Applied Logic 2018] are used, extended, define an equivalence categories. Finally, couple examples studied with these new tools.
منابع مشابه
A Simplicial Description of the Homotopy Category of Simplicial Groupoids
In this paper we use Quillen’s model structure given by Dwyer-Kan for the category of simplicial groupoids (with discrete object of objects) to describe in this category, in the simplicial language, the fundamental homotopy theoretical constructions of path and cylinder objects. We then characterize the associated left and right homotopy relations in terms of simplicial identities and give a si...
متن کاملQ-groupoids and Their Cohomology
We approach Mackenzie’s LA-groupoids from a supergeometric point of view by introducing Q-groupoids. A Q-groupoid is a groupoid object in the category of Q-manifolds, and there is a faithful functor from the category of LA-groupoids to the category of Q-groupoids. Using this approach, we associate to every LA-groupoid a double complex whose cohomology simultaneously generalizes Lie groupoid coh...
متن کاملClosed model categories for presheaves of simplicial groupoids and presheaves of 2-groupoids
We prove that the category of presheaves of simplicial groupoids and the category of presheaves of 2-groupoids have Quillen closed model structures. We also show that the homotopy categories associated to the two categories are equivalent to the homotopy categories of simplicial presheaves and homotopy 2-types, respectively.
متن کاملTHE DOLD-KAN CORRESPONDENCE 1. Simplicial sets
We have just seen that the category ∆ is equivalent to the subcategory consisting of the [n]. As a result, a simplicial set X• is given by specifying sets Xn for each n ∈ Z≥0, together with maps Xn → Xm for each map [m] → [n] in ∆. These maps are required to satisfy compatibility conditions (i.e., form a functor). The set Xn is called the set of n-simplices of X•. Example 1.3. Let X be a topolo...
متن کاملExtending Datalog to cover XQuery
Datalog is a traditional platform in database research and, due to its ability to comprehend recursion, it seems to be a good choice for modeling XQuery. Unfortunately, XQuery functions have arguments carrying sequences; therefore, logic-based models of XQuery must be second-order languages and, consequently, Datalog is usually extended by node-set variables. In this paper, we suggest an altern...
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: Annals of Pure and Applied Logic
سال: 2021
ISSN: ['0168-0072', '1873-2461']
DOI: https://doi.org/10.1016/j.apal.2021.102970