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# Trace Semantics for Coalgebras

@article{Jacobs2004TraceSF, title={Trace Semantics for Coalgebras}, author={Bart Jacobs}, journal={Electr. Notes Theor. Comput. Sci.}, year={2004}, volume={106}, pages={167-184} }

- Published 2004 in Electr. Notes Theor. Comput. Sci.
DOI:10.1016/j.entcs.2004.02.031

Traditionally, traces are the sequences of labels associated with paths in transition systems X → P(A×X). Here we describe traces more generally, for coalgebras of the form X → P(F (X)), where F is a polynomial functor. The main result states that F ’s final coalgebra Z ∼= −→ F (Z) gives rise to a weakly final coalgebra with state space P(Z), in a suitable category of coalgebras. Weak finality means that there is a coalgebra map X → P(Z), but there is no uniqueness. We show that there is a… CONTINUE READING