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Finitary fibrations

Grzegorz Jarzembski (1989)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Modular dynamical systems on networks

Lee DeVille, Eugene Lerman (2015)

Journal of the European Mathematical Society

We propose a new framework for the study of continuous time dynamical systems on networks. We view such dynamical systems as collections of interacting control systems. We show that a class of maps between graphs called graph fibrations give rise to maps between dynamical systems on networks. This allows us to produce conjugacy between dynamical systems out of combinatorial data. In particular we show that surjective graph fibrations lead to synchrony subspaces in networks. The injective graph fibrations,...

On associated and attached prime ideals of certain modules

K. Divaani-Aazar (2001)

Colloquium Mathematicae

Primary and secondary functors have been introduced in [2] and applied to extend some results concerning asymptotic prime ideals. In this paper, the theory of primary and secondary functors is developed and examples of non-exact primary and non-exact secondary functors are presented. Also, as an application, the sets of associated and of attached prime ideals of certain modules are determined.

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...

On pure quotients and pure subobjects

Jiří Adámek, Jiří Rosický (2004)

Czechoslovak Mathematical Journal

In the theory of accessible categories, pure subobjects, i.e. filtered colimits of split monomorphisms, play an important role. Here we investigate pure quotients, i.e., filtered colimits of split epimorphisms. For example, in abelian, finitely accessible categories, these are precisely the cokernels of pure subobjects, and pure subobjects are precisely the kernels of pure quotients.

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