Related papers: Elementary quotient completion
We consider the problem of extending maps from algebras to their profinite completions in finitely generated quasivarieties. Our developments are based on the construction of the profinite completion of an algebra as its natural extension.…
We characterize when the elementary diagram of a mutually algebraic structure has a model complete theory, and give an explicit description of a set of existential formulas to which every formula is equivalent. This characterization yields…
We introduce a new version of arithmetic in all finite types which extends the usual versions with primitive notions of extensionality and extensional equality. This new hybrid version allows us to formulate a strong form of extensionality,…
This note proposes a new method to complete a triangulated category, which is based on the notion of a Cauchy sequence. We apply this to categories of perfect complexes. It is shown that the bounded derived category of finitely presented…
Trees are partial orderings where every element has a linearly ordered set of smaller elements. We define and study several natural notions of completeness of trees, extending Dedekind completeness of linear orders and Dedekind-MacNeille…
We give an answer to the following question: for which metric in an abstract lattice the completion as a metric space coincides with the completion as a lattice. We obtain the answer for inductive limits of lattices which are complete in…
We ask whether the operational quantum description is complete at the level of preparations: can the empirically accessible properties of a finite preparation set be reproduced exactly by a hidden-variable description, or must every such…
We prove two completeness results for Kleene algebra with tests and a top element, with respect to guarded string languages and binary relations. While the equational theories of those two classes of models coincide over the signature of…
We study the succinctness of the complement and intersection of regular expressions. In particular, we show that when constructing a regular expression defining the complement of a given regular expression, a double exponential size…
We show that every additive category with kernels and cokernels admits a maximal exact structure. Moreover, we discuss two examples of categories of the latter type arising from functional analysis.
We introduce a new class of extensions of terms that consists in navigation strategies and insertion of contexts. We introduce an operation of combination on this class which is associative, admits a neutral element and so that each…
Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…
The reflexive completion of a category consists of the Set-valued functors on it that are canonically isomorphic to their double conjugate. After reviewing both this construction and Isbell conjugacy itself, we give new examples and revisit…
We analyse limits and colimits in the category $Part$ of partial groups, algebraic structures introduced by A. Chermak. We will prove that $Part$ is both complete and cocomplete and, in addition, that the full subcategory of finite partial…
We extend some of our earlier results on the interconnection between ultrafilter extensions, and ultrapowers. Throughout we restrict ourselves to relational structures with one binary relation. Recently it was shown that for bounded…
Using the Morita-type embedding, we show that any exact category with enough projectives has a realization as a (pre)resolving subcategory of a module category. When the exact category has enough injectives, the image of the embedding can…
We find the model completion of the theory modules over $A$, where $A$ is a finitely generated commutative algebra over a field $K$. This is done in a context where the field $K$ and the module are represented by sorts in the theory, so…
We investigate equivalences between the categories of perfects complexes of the quotients of two smooth projective schemes by the action of a finite group. As a result we give a necessary and sufficient condition for an equivalence between…
The category of models of any theory $T$ in any first-order language $L$ has the surprising property that any small category that is elementarily equivalent with it, already embeds in it. The proof uses an abstract argument via ultrapowers,…
We consider the problem of completing a matrix with categorical-valued entries from partial observations. This is achieved by extending the formulation and theory of one-bit matrix completion. We recover a low-rank matrix $X$ by maximizing…