Multilinear representations of free pros

ABSTRACT

We describe a structure of pro on hypermatrices. This structure allows us to define multilinear representations of pros and in particular of free pros. As an example of applications, we investigate the relations of the representations of pros with the theory of automata.

COMMUNICATED BY:

• Lajos Molnar

Keywords:

• Pros
• operads
• hypermatrices
• categories
• theory of automata

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 In the algebraic definition, these morphisms are monoidal functors.

2 The Eckmann–Hilton argument states that if a set X is endowed with two unital binary operations · and ⋆ satisfying $(a\star b)\cdot (c\star d)=(a\cdot c)\star (b\cdot d)$, then ⋆ and · are the same commutative and associative operation.

Additional information

Funding

This work was partially supported by ERDF project MOUSTIC [HN0005610] and RIN project ARTIQ.