Related papers: The effective model structure and $\infty$-groupoi…

We present applications of contramodule techniques to the Enochs conjecture about covers and direct limits, both in the categorical tilting context and beyond. In the $n$-tilting-cotilting correspondence situation, if $\mathsf A$ is a…

As a practical foundation for a homotopy theory of abstract spacetime, we extend a category of certain compact partially ordered spaces to a convenient category of locally preordered spaces. In particular, we show that our new category is…

In a recent paper we introduced a much weaker and easy to verify structure than a model category, which we called a "weak fibration category". We further showed that a small weak fibration category can be "completed" into a full model…

We show that Quillen's small object argument works for exact categories under very mild conditions. This has immediate applications to cotorsion pairs and their relation to the existence of certain triangulated adjoint functors and model…

For a small category K enriched over a suitable monoidal category V, the free completion of K under colimits is the presheaf category [K*,V]. If K is large, its free completion under colimits is the V-category PK of small presheaves on K,…

Let $A$ be the path algebra of a quiver of Dynkin type $\mathbb{A}_n$. The module category $\text{mod}\,A$ has a combinatorial model as the category of diagonals in a polygon $S$ with $n+1$ vertices. The recently introduced notion of almost…

Suppose that $F: \mathcal{N} \to \mathcal{M}$ is a functor whose target is a Quillen model category. We give a succinct sufficient condition for the existence of the right-induced model category structure on $\mathcal{N}$ in the case when…

Existentially closed groups are, informally, groups that contain solutions to every consistent finite system of equations and inequations. They were introduced in 1951 in an algebraic context and subsequent research elucidated deep…

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…

This article mentions that Smith ideal theory generalizes the adic completion theory of commutative rings to monoid objects of locally presentable symmetric monoidal abelian categories. As an application, we provide an almost mathematics…

We show that any closed model category of simplicial algebras over an algebraic theory is Quillen equivalent to a proper closed model category. By ``simplicial algebra'' we mean any category of algebras over a simplicial algebraic theory,…

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 call a finitely complete category algebraically coherent when the change-of-base functors of its fibration of points are coherent, which means that they preserve finite limits and jointly strongly epimorphic pairs of arrows. We give…

We investigate the question of when free structures of infinite rank (in a variety) possess model-theoretic properties like categoricity in higher power, saturation, or universality. Concentrating on left $R$-modules we show, among other…

We derive a new sufficient condition for the existence of {\omega}-categorical universal structures in classes of relational structures with constraints, augmenting results by Cherlin, Shelah, Chi, and Hubi\v{c}ka and Ne\v{s}et\v{r}il.…

Let $H$ be a group and $E$ a set such that $H \subseteq E$. We shall describe and classify up to an isomorphism of groups that stabilizes $H$ the set of all group structures that can be defined on $E$ such that $H$ is a subgroup of $E$. A…

We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme with…

In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete…

We study positively closed and strongly positively closed topos-valued models of coherent theories. Positively closed is a global notion (it is defined in terms of all possible outgoing homomorphisms), while strongly positively closed is a…

We introduce a model category of spaces based on the definable sets of an o-minimal expansion of a real closed field. As a model category, it resembles the category of topological spaces, but its underlying category is a coherent topos. We…