13 citations · 19 across the 19 of their papers we have counts for
19 papers
A first-order theory is stable iff its type space is simplicially contractible
Misha Gavrilovich
A definable type of a first-order theory is the same as a section (retraction) of the simplicial path space (decalage) of its space of types viewed as a simplicial topological spac…
Extremally disconnected spaces as {{u->a,b<-v}-->{u->a=b<-v}}^l, and being proper as ({{o}-->{o->c}}^r_<4)^lr
M. Gavrilovich
We observe that the notions of a topological space being extremally disconnected, and of a continuous map of compact Hausdorff spaces being proper, and being surjective proper, can…
Remarks on Shelah's classification theory and Quillen's negation
Misha Gavrilovich
We give category-theoretic reformulations of stability, NIP, NTP, and non-dividing by observing that their characterisations in terms of indiscernible sequences are naturally expre…
Geometric realisation as the Skorokhod semi-continuous path space endofunctor
Misha Gavrilovich, Konstantin Pimenov
We interpret a construction of geometric realisation by [Besser], [Grayson], and [Drinfeld] of a simplicial set as constructing a space of maps from the interval to a simplicial se…
Simplicial sets with a notion of smallness
M. Gavrilovich
We consider simplicial sets equipped with a notion of smallness, and observe that this slight "topological" extension of the "algebraic" simplicial language allows a concise reform…
Formulating basic notions of finite group theory via the lifting property
Misha Gavrilovich
We reformulate several basic notions of notions in finite group theory in terms of iterations of the lifting property (orthogonality) with respect to particular morphisms. Our exam…
Standard conjectures in model theory, and categoricity of comparison isomorphisms
Misha Gavrilovich
We formulate two conjectures about etale cohomology and fundamental groups motivated by categoricity conjectures in model theory. One conjecture says that there is a unique Z-form…
A naive diagram-chasing approach to formalisation of tame topology
Misha Gavrilovich, Konstantin Pimenov
We rewrite classical topological definitions using the category-theoretic notation of arrows and are led to concise reformulations in terms of simplicial categories and orthogonali…
Topological and metric spaces are full subcategories of the category of simplicial objects of the category of filters
Misha Gavrilovich
We observe that the category of topological space, uniform spaces, and simplicial sets are all, in a natural way, full subcategories of the same larger category, namely the simplic…
The unreasonable power of the lifting property in elementary mathematics
Misha Gavrilovich
We illustrate the generative power of the lifting property (orthogonality of morphisms in a category) as means of defining natural elementary mathematical concepts by giving a numb…
Separation axioms as lifting properties
Misha Gavrilovich
We observe that many of the separation axioms of topology (including ) can be expressed concisely and uniformly in terms of category theory as lifting properties (in the s…
Expressing the statement of the Feit-Thompson theorem with diagrams in the category of finite groups
Misha Gavrilovich
We reformulate the statement of the Feit-Thompson theorem in terms of diagrams in the category of finite groups, namely iterations of the Quillen lifting property with respect to p…
Point-set topology as diagram chasing computations: Lifting property as negation
Misha Gavrilovich
We observe that some natural mathematical definitions are lifting properties relative to simplest counterexamples, namely the definitions of surjectivity and injectivity of maps, a…
Exercices de style: A homotopy theory for set theory II
Misha Gavrilovich, Assaf Hasson
This is the second part of a work initiated in \cite{GaHa}, where we constructed a model category, $\Qt$, for set theory. In the present paper we use this model category to introdu…
Some Definability Results in Abstract Kummer Theory
Martin Bays, Misha Gavrilovich, Martin Hils
Let be a semiabelian variety over an algebraically closed field, and let be an irreducible subvariety not contained in a coset of a proper algebraic subgroup of . We sho…
The univalence axiom in posetal model categories
Misha Gavrilovich, Assaf Hasson, Itay Kaplan
In this note we interpret Voevodsky's Univalence Axiom in the language of (abstract) model categories. We then show that any posetal locally Cartesian closed model category in…
A homotopy approach to set theory
Misha Gavrilovich
We observe that the notion of two sets being equal up to finitely many elements is a homotopy equivalence relation in a model category, and suggest a homotopy-invariant variant of…
Covers of Abelian varieties as analytic Zariski structures
Misha Gavrilovich
We use tools of mathematical logic to analyse the notion of a path on an complex algebraic variety, and are led to formulate a "rigidity" property of fundamental groups specific to…
A remark on transitivity of Galois action on the set of uniquely divisible abelian extensions of the group of algebraic points of an elliptic curve, by
Misha Gavrilovich
We study Galois action on $\Ext^1(E(\bar \Q),\Z^2)$ and interpret our results as partially showing that the notion of a path on a complex elliptic curve can be characterised al…