We introduce signed exceptional sequences as factorizations of morphisms in the cluster morphism category. The objects of this category are wide subcategories of the module category of a hereditary algebra. A morphism [T ] : A → B is an equivalence class of rigid objects T in the cluster category of A so that B is the right hom-ext perpendicular category of the underlying object |T | ∈ A. Facto...

we find a criterion for a morphism of coalgebras over a barr-exact category to be effective descent and determine (effective) descent morphisms for coalgebras over toposes in some cases. also, we study some exactness properties of endofunctors of arbitrary categories in connection with natural transformations between them as well as those of functors that these transformations induce between co...

In this paper we study single-pushout transformation in a category of spans, a generalization of the notion of partial morphism in, for instance, 2,4]. As an application, single-pushout transformation in a category of hypergraphs with a special type of partial morphisms, the conformisms, is presented. In particular , we show the existence of the pushout of any pair of conformisms of hypergraphs...

‎In this paper first we define the morphism between geometric spaces in two different types‎. ‎We construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories‎, ‎for instance $uu$ is topological‎. ‎The relation between hypergroups and geometric spaces is studied‎. ‎By constructing the category $qh$ of $H_{v}$-groups we answer the question...

In this paper C denotes a category and o1, o2, o3 denote objects of C. Let C be a non empty category structure with units and let o be an object of C. Observe that 〈o, o〉 is non empty. The following propositions are true: (1) Let v be a morphism from o1 to o2, u be a morphism from o1 to o3, and f be a morphism from o2 to o3. If u = f · v and f −1 · f = id(o2) and 〈o1, o2〉 6= ∅ and 〈o2, o3〉 6= ∅...

It is proved that in any pointed category with pullbacks, coequalizers and regular epi-mono factorizations, the class of regular epimorphisms is stable under pullback along the so-called balanced effective descent morphisms. Here “balanced” can be omitted if the category is additive. A balanced effective descent morphism is defined as an effective descent morphism p : E → B such that any subobj...

A logic is developed in which function symbols are allowed to represent partial functions. It has the usual rules of logic (in the form of a sequent calculus) except that the substitution rule has to be modi ed. It is developed here in its minimal form, with equality and conjunction, as partial Horn logic . Various kinds of logical theory are equivalent: partial Horn theories, quasi-equational ...

In this paper we present the problem of saturation of a given morphism in the database category DB, which is the base category for the functiorial semantics of the database schema mapping systems used in Data Integration theory. This phenomena appears in the case when we are using the Second-Order tuple-generating dependencies (SOtgd) with existentially quantified non-built-in functions, for th...

Directed containers make explicit the additional structure of those containers whose set functor interpretation carries a comonad structure. The data and laws of a directed container resemble those of a monoid, while the data and laws of a directed container morphism those of a monoid morphism in the reverse direction. With some reorganization, a directed container is the same as a small catego...