Abstract
This paper is towards studying L-fuzzy automata, coalgebras, and dialgebras from categorical and L-fuzzy topological points of view, where L is a complete residuated lattice. Specifically, we introduce the categories of coalgebras and dialgebras and show that the category of L-fuzzy automata is categories of coalgebras and dialgebras, respectively. Further, we establish the relationships among the L-fuzzy languages recognized by L-fuzzy automata, coalgebras, and dialgebras and study bisimulation between coalgebras. Interestingly, L-fuzzy languages recognized by L-fuzzy automaton, coalgebra, and dialgebra are enriched with L-fuzzy co-topologies and L-fuzzy topologies.
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