Abstract Multipath cohomology is a theory for directed graphs, which defined using the path poset. The aim of this paper to investigate combinatorial properties posets and provide computational tools multipath cohomology. In particular, we develop acyclicity criteria computations groups oriented linear graphs. We further interpret poset as face simplicial complex, realisability problems.

Fuzzy order congruences play an important role in studying the categoricalproperties of fuzzy posets. In this paper, the correspondence between the fuzzyorder congruences and the fuzzy order-preserving maps is discussed. We focus onthe characterization of fuzzy order congruences on the fuzzy poset in terms ofthe fuzzy preorders containing the fuzzy partial order. At last, fuzzy completecongruen...

It is a classic result in lattice theory that a poset is a complete lattice i↵ it can be realized as fixpoints of a closure operator on a powerset. Dragalin [9,10] observed that a poset is a locale (complete Heyting algebra) i↵ it can be realized as fixpoints of a nucleus on the locale of upsets of a poset. He also showed how to generate a nucleus on upsets by adding a structure of “paths” to a...

We study the so-called Skorokhod reflection problem (SRP) posed for real-valued functions defined on a partially ordered set (poset), when there are two boundaries, considered also to be functions of the poset. The problem is to constrain the function between the boundaries by adding and subtracting nonnegative nondecreasing (NN) functions in the most efficient way. We show existence and unique...