Abstract:
The article considers the construction of homotopy steady analog of simplicial object. The author introduces a design of highest simplicial operators and proves a theorem of their existence on chain complex homologies. The proof of the existence theorem is constructive, which allows to build the received highest simplicial sets as homotopy steady analogs, that are simplicial on chain complex homologies.
Keywords:simplicial object, homology, homology stability, SDR-situation, the higher simplicial operators.