Non-standard sequences

The paper shows the existence of a previously unknown relationship between the theory of monoids and category theory. A non-standard mathematical method based on terms from non-standard (not always existing) sequences is proposed. In the article in particular are proved the following statement: Every category is a complete model of some monoid with an associative zero. Conversely, any such monoid completely models some category. Category theory is logically equivalent to the theory of monoids with an associative zero. Both are non-essential extensions of each other. (Theorem 1)