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On corings and comodules

Hans-Eberhard Porst (2006)

Archivum Mathematicum

It is shown that the categories of R -coalgebras for a commutative unital ring R and the category of A -corings for some R -algebra A as well as their respective categories of comodules are locally presentable.

On derived equivalence classification of gentle two-cycle algebras

Grzegorz Bobiński, Piotr Malicki (2008)

Colloquium Mathematicae

We classify, up to derived (equivalently, tilting-cotilting) equivalence, all nondegenerate gentle two-cycle algebras. We also give a partial classification and formulate a conjecture in the degenerate case.

On dual Ramsey theorems for relational structures

Dragan Mašulović (2020)

Czechoslovak Mathematical Journal

We discuss dual Ramsey statements for several classes of finite relational structures (such as finite linearly ordered graphs, finite linearly ordered metric spaces and finite posets with a linear extension) and conclude the paper with another rendering of the Nešetřil-Rödl Theorem for relational structures. Instead of embeddings which are crucial for ``direct'' Ramsey results, for each class of structures under consideration we propose a special class of quotient maps and prove a dual Ramsey theorem...

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