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In category theory, a (strict) n-monoid is an n-category with only one 0-cell. In particular, a 1-monoid is a monoid and a 2-monoid is a strict monoidal category.
References

Albert Burroni (1993). Higher dimensional word problems with applications to equational logic (PDF). Theoretical Computer Science.

Further reading

n-monoid in nLab

Mathematics Encyclopedia

Hellenica World - Scientific Library

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