FUNGTORIALITAS DAN ISOMORFISMA ALJABAR INSIDENSI SUATU PARTIALLY ORDERED SET (POSET )

In forming a functor from category of poset to category of algebra, a relation of object and morphism on these categories is needed. Category of incidence algebra is a part of category of algebra. From the poset and commutative ring can be formed an incidence algebra. In general, a morphism on category of poset does not induce morphism on incidence algebra. This implies that the functor formed is not well-generated. There are two methods that have been done to make it running well, first is to define a bimodule on incidence algebra that functioned as the morphism, and second to restrict the poset so that it works on simplicial complexes. In this disertation a new functor is generated: a functor from category of poset to category of simplicial complexes. This is made in order to get a functor from the category of Poset to the category of algebra by using functor composition. In general incidence algebra is defined on locally finite poset so that the multiplicative operation is well-defined. In this disertation, a new definition of incidence algebra is defined on an abritarary poset, but with an additional requirement, that is the finite of its sub poset, so that the incidence algebra can be defined, called finitary incidence algebra. With this new definition, it is found that a covariant functor from category of poset to incidence algebra is obtained, and some isomorphism problems on finitary incidence algebra can be solved by applying this definition. In particular, for potentially isomorphic problem, there must be some additional requirement on one of the poset. Covariant functor can be found from the category of simplicial complexes to the category of abelian groups. The functor is simplicial chain group, which is the sequence of them will form a simplicial chain complex. Morphism which assign simplicial chain complex is simplicial chain map, and finally the new category called category of simplicial chain complex can be obtained