Related papers: Quasitoposes as elementary quotient completions
We discuss the asymptotic structure of spacetimes, presenting a new construction of ideal points at infinity and introducing useful topologies on the completed space. Our construction is based on structures introduced by Geroch, Kronheimer,…
We treat equivariant completions of toric contraction morphisms as an application of the toric Mori theory. For this purpose, we generalize the toric Mori theory for non-$\mathbb Q$-factorial toric varieties. So, our theory seems to be…
We generalize a well-known theorem binding the elementary equivalence relation on the level of PAC fields and the isomorphism class of their absolute Galois groups. Our results concern two cases: saturated PAC structures and non-saturated…
The article is devoted to holomorphic and meromorphic functions of quaternion and octonion variables. New classes of quasi-conformal and quasi-meromorphic mappings are defined and investigated. Properties of such functions such as their…
For any small quantaloid $\Q$, there is a new quantaloid $\D(\Q)$ of diagonals in $\Q$. If $\Q$ is divisible then so is $\D(\Q)$ (and vice versa), and then it is particularly interesting to compare categories enriched in $\Q$ with…
Following an idea of Kontsevich, we introduce and study the notion of formal completion of a compactly generated (by a set of objects) enhanced triangulated category along a full thick essentially small triangulated subcategory. In…
We contribute to the knowledge of the quantifier completions and their applications by using the language of doctrines. This algebraic presentation allows us to properly analyse the behaviour of the existential and universal quantifiers. We…
We introduce the notion of topological entropy of a formal languages as the topological entropy of the minimal topological automaton accepting it. Using a characterization of this notion in terms of approximations of the Myhill-Nerode…
There are many category-theoretic notions of algebraic theory, including Lawvere theories, monads, PROPs and operads. The first central notion of this thesis is a common generalisation of these, which we call a proto-theory. In order to…
Linearly repetitive cut and project sets are mathematical models for perfectly ordered quasicrystals. In a previous paper we presented a characterization of linearly repetitive cut and project sets. In this paper we extend the classical…
Many ex/reg completions $J:\mathcal C\to\mathcal C_{\rm ex/reg}$ that arise in categorical realizability and tripos theory admit left Kan extensions of arbitrary finitely continuous functors to arbitrary exact categories. This paper…
We study the relationship between presheaf constructions and free cocompletions in the context of formal category theory, elucidating the coincidence between the two concepts in familiar settings. We show that, in a virtual equipment…
In his 2008 thesis, Tateno claimed a counterexample to the Bonato-Tardif conjecture regarding the number of equimorphy classes of trees. In this paper we revisit Tateno's unpublished ideas to provide a rigorous exposition, constructing…
We prove Koebe's conjecture and a version of Schramm's cofat uniformization theorem for domains $\Omega \subset \mathbb C$ satisfying conditions involving quasitripods, i.e., quasisymmetric images of the standard tripod. If the non-point…
For all classical groups (and for their analogs in infinite dimension or over general base fields or rings) we construct certain contractions, called "homotopes". The construction is geometric, using as ingredient involutions of associative…
For all classical groups (and for their analogs in infinite dimension or over general base fields or rings) we construct certain contractions, called "homotopes". The construction is geometric, using as ingredient involutions of associative…
The so-called topos approach provides a radical reformulation of quantum theory. Structurally, quantum theory in the topos formulation is very similar to classical physics. There is a state object, analogous to the state space of a…
A classical tensor product $A \,\otimes\, B$ of complete lattices $A$ and $B$, consisting of all down-sets in $A \times B$ that are join-closed in either coordinate, is isomorphic to the complete lattice $Gal(A,B)$ of Galois maps from $A$…
We characterise the (closeness classes of) quasi-isometric embeddings as the regular monomorphisms in the coarsely Lipschitz category, formalising the notion that they are isomorphisms onto their image. Furthermore, we prove that the…
An element $a$ of a lattice cups to an element $b > a$ if there is a $c < b$ such that $a \cup c = b$. An element of a lattice has the cupping property if it cups to every element above it. We prove that there are non-zero honest elementary…