Related papers: The Flat Cover Conjecture for Monoid Acts
Consider a diagram of quasi-categories that admit and functors that preserve limits or colimits of a fixed shape. We show that any weighted limit whose weight is a projective cofibrant simplicial functor is again a quasi-category admitting…
In this paper, we prove a version of Freyd's generating hypothesis for triangulated categories: if D is a cocomplete triangulated category and S is an object in D whose endomorphism ring is graded commutative and concentrated in degree…
The purpose of this paper is to introduce the theory of presentations of monoids acts. We aim to construct `nice' general presentations for various act constructions pertaining to subacts and Rees quotients. More precisely, given an $M$-act…
In this paper, we classify finite categories with two objects such that one of the endomorphism monoids is a group. We prove that having a group on one side affects the structure of the other endomorphism monoid, and we prove that it is…
In this paper, we introduce (Rees) artinian S-acts as those acts that satisfy the descending chain condition on their (Rees) congruences. Then, we show that artinian S-acts are those acts whose all factor acts are finitely (Rees)…
We study congruences on the partial automorphism monoid of a finite rank free group action. We give a decomposition of a congruence on this monoid into a Rees congruence, a congruence on a Brandt semigroup and an idempotent separating…
We show that a direct limit of projective contramodules (over a right linear topological ring) is projective if it has a projective cover. A similar result is obtained for $\infty$-strictly flat contramodules of projective dimension not…
This paper investigates the class of finitely presented monoids defined by homogeneous (length-preserving) relations from a computational perspective. The properties of admitting a finite complete rewriting system, having finite derivation…
We provide conditions on a monoidal model category $\mathcal{M}$ so that the category of commutative monoids in $\mathcal{M}$ inherits a model structure from $\mathcal{M}$ in which a map is a weak equivalence or fibration if and only if it…
Let $S$ be a submonoid of a free Abelian group of finite rank. We show that if $k$ is a field of prime characteristic such that the monoid $k$-algebra $k[S]$ is split $F$-regular, then $k[S]$ is a finitely generated $k$-algebra, or…
Given a small category $I$ and a closed symmetric monoidal category $\mm$, we show that the diagram category $\mm^I$ with the objectwise product is a closed symmetric monoidal category. We then prove that if $I$ is a Reedy category and…
The main purpose of the present work is an investigation of the notions Hopfian (co-Hopfian) acts whose their surjective (injective) endomorphisms are isomorphisms. While we investigate conditions that are relevant to these classes of acts,…
Let $S$ be a surface of finite type which is not a sphere with at most four punctures, a torus with at most two punctures, or a closed surface of genus two. Let $\mathcal{MF}$ be the space of equivalence classes of measured foliations of…
Wright showed that, if a 1-ended simply connected locally compact ANR Y with pro-monomorphic fundamental group at infinity admits a proper Z-action, then that fundamental group at infinity can be represented by an inverse sequence of…
In this paper, cogenerating classes of $S$-acts are introduced as those that can be used to cogenerate $S$-acts in an appropriate sense. Next, finitely cogenerated $S$-acts are introduced. Such an $S$-act is then characterized as one whose…
We consider classes $ \mathcal{A}_M(S) $ of functions holomorphic in an open plane sector $ S $ and belonging to a strongly non-quasianalytic class on the closure of $ S $. In $ \mathcal{A}_M(S) $, we construct functions which are flat at…
The first author showed in a previous paper that there is a correspondence between self-similar group actions and a class of left cancellative monoids called left Rees monoids. These monoids can be constructed either directly from the…
We introduce a new class of finite groups, called weak almost monomial, which generalize two different notions of "almost monomial" groups, and we prove it is closed under taking factor groups and direct products. Let $K/\mathbb Q$ be a…
We prove a structure result on proper extensions of two-sided restriction semigroups in terms of partial actions, generalizing respective results for monoids and for inverse semigroups and upgrading the latter. We introduce and study…
A new notion of independence relation is given and associated to it, the class of flat theories, a subclass of strong stable theories including the superstable ones is introduced. More precisely, after introducing this independence…