A calculus of transition systems (towards universal coalgebra)

By representing transition systems as coalgebras, the three main ingredients of their theory: coalgebra, homomorphism, and bisimulation, can be seen to be in a precise correspondence to the basic notions of universal algebra: Sigma-algebra, homomorphism, and substitutive relation (or congruence). In this paper, some standard results from universal algebra (such as the three isomorphism theorems and facts on the lattices of subalgebras and congruences) are reformulated (using the afore mentioned correspondence) and proved for transition systems.