The Topology of Syntax Relations of a Formal Language

The method of constructing of Grothendieck’s topology basing on a neighbourhood grammar, defined on the category of syntax diagrams is described in the article. Syntax diagrams of a formal language are the multigraphs with nodes, signed by symbols of the language’s alphabet. The neighbourhood grammar allows to select correct syntax diagrams from the set of all syntax diagrams on the given alphabet by mapping an each correct diagram to the cover consisted of the grammar’s neighbourhoods. Such the cover gives rise to Grothendieck’s topology on category Ext(DG) of correct syntax diagrams extended by neighbourhoods’ diagrams. An each object of category Ext(DG) may be mapped to the set of meanings (abstract senses) of this syntax construction. So, the contrvariant functor from category Ext(DG) to category of sets Sets is defined. The given category SetsG op likes to be seen as the convenient means to think about relations between syntax and semantic of a formal language. The sheaves of set defined on category Ext(DG) are the objects of category Sets Ext(DG) op that satisfy of compositionality principle defined in the semantic anal-