The Kernel Category and Variants of the Concatenation Product
Mário J. J. Branco · International Journal of Algebra and Computation · 1997
For each variety V of finite monoids, we consider three varieties [Formula: see text] of languages defined in the following way: for each alphabet [Formula: see text] is the Boolean algebra generated by the languages of the form L or L0aL1, where [Formula: see text], a ∈ A and the product L0aL1 is deterministic (resp. codeterministic, bideterministic). We present a description of the corresponding varieties of finite monoids. Such descriptions are done in terms of categories, using the kernel category of a relational morphism. We also give some connections with the positive varieties of languages and with the varieties of finite ordered monoids.