Elementary and multielementary representations of vectroids

Functors and dyadic sets of finite type

“…We set dim 3v= sup~r A. In fact, the following result is well known [1,4] Generally, $/and ind V are not uniquely determined by the completed boset S~. However, if I-III hold, then an isomorphism between S~v I and S~2 induces a one-to-one correspondence between ind ~ and ind ~v~ [4].…”

On corepresentations of one parametric equipped posets

“…Proof. Since both statements of the Theorem are self-dual, we proof only one of them, for instance (1). We breaking up the proof into four cases.…”

Finitely represented dyadic sets and their multielementary representations

“…Note that, for any dyadic set S, it is possible to construct a vectroid (a subcategory of mod k that is a spectroid in terms of [2]) qfl = VectS [3] …”

“…In [1,5], the main statement ([2], 5.8) was proved: IIndSI < ~ iff ]Ind C(S) I < o~. For a special case, it was proved in [3]; here is only one (up to equivalence and duality) nonmultielementary indecomposable Ex. In the general case, nonmultielementary representations of finitely represented S are, in a certain sense, modifications of Ex; they were classified in [6,7].…”

“…1). The representations in Im | are called multielementary [3] (normal [4]). In [1,5], the main statement ([2], 5.8) was proved: IIndSI < ~ iff ]Ind C(S) I < o~.…”