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math.RA2026
Faithful linear and relational representations of diagram categories and monoids
James East, Marianne Johnson, Mark Kambites
We study representations of diagram categories by binary relations and matrices over rings and semirings. Our main result is a faithful involutive tensor representation of the part…
math.RA2026
Semirings of formal sums and injective partial transformations
Maximilien Gadouleau, Marianne Johnson
The semiring of discrete dynamical systems is a simple algebraic model for modularity in deterministic systems. The objects of the semiring are finite transformations (viewed as di…