Characterization of coextensive varieties of universal algebras

Coextensive varieties via Central Elements

In this paper we use the theory of central elements in order to provide a characterization for coextensive varieties. In particular, if the variety is of finite type, congruence-permutable and its class of directly indecomposable members is universal, then coextensivity is equivalent to be a variety of shells.

Characterization of coextensive varieties of universal algebras II

A coextensive category can be defined as a category $\mathcal{C}$ with finite products such that for each pair $X,Y$ of objects in $\mathcal{C}$, the canonical functor $\times\colon X/\mathcal{C} \times Y/\mathcal{C} \to (X \times Y)/\mathcal{C}$ is an equivalence. We give a syntactical characterization of coextensive varieties of universal algebras. This paper is an updated version of the pre-print arXiv:2008.03474

从共延展变种到Gaeta位面

From coextensive varieties to the Gaeta topos

本文研究了共延展变种中中心元素的函子性质，并证明在特定条件下Gaeta位面可分类无中心模型。

$\mathcal{M}$-coextensivity and the strict refinement property

The notion of an $\mathcal{M}$-coextensive object is introduced in an arbitrary category $\mathbb{C}$, where $\mathcal{M}$ is a distinguished class of morphisms from $\mathbb{C}$. This notion allows for a categorical treatment of the strict refinement property in universal algebra, and highlights its connection with extensivity in the sense of Carboni, Lack and Walters. If $\mathcal{M}$ is the class of all product projections in a variety of algebras $\mathbb{C}$, then the $\mathcal{M}$-coextensive (or projection-coextensive) objects in $\mathbb{C}$ turn out to be precisely those algebras whic…

关于态射的广延性

On extensivity of morphisms

本文提出广延态射与余广延态射概念，将泛代数性质范畴化，并证明 Barr-正合范畴余广延当且仅当其所有分裂单态射均余广延。

Effective codescent morphisms in some varieties of universal algebras

The paper gives the sufficient condition formulated in the syntactical form for all codescent morphisms of a variety of universal algebras satisfying the amalgamation property to be effective. This result is further used in proving that all codescent morphisms of quasigroups are effective.