Ziegler partial morphisms in additive exact categories

Partial Morphisms in Categories of Effective Objects

Graph Rewriting in Some Categories of Partial Morphisms

We present a definition of term graph rewriting as the taking of a pushout in a category of partial morphisms, adapting the rather ad hoc definitions we gave in [Ken87] so as to use a standard category-theoretic concept of partial morphism. This single-pushout construction is shown to coincide with the well-known double-pushout description of graph rewriting whenever the latter is defined. In g...

Triangulated categories and the Ziegler spectrum

Covering Morphisms in Categories of Relational Algebras

In this paper we use Janelidze’s approach to the classical theory of topological coverings via categorical Galois theory to study coverings in categories of relational algebras. Moreover, we present characterizations of effective descent morphisms in the categories of M ordered sets and of multi-ordered sets.

Finitely Presentable Morphisms in Exact Sequences

Let K be a locally finitely presentable category. If K is abelian and the sequence 0 K // X // k // C c // // 0 // is short exact, we show that 1) K is finitely generated⇔ c is finitely presentable; 2) k is finitely presentable⇔ C is finitely presentable. The “⇐” directions fail for semi-abelian varieties. We show that all but (possibly) 2)(⇐) follow from analogous properties which hold in all ...