Step 1: Understanding pyran.
Pyran is a six-membered ring compound containing one oxygen atom and five carbon atoms.
Step 2: Nature of the ring.
Since an oxygen atom is present in the ring, pyran is classified as a heterocyclic compound.
Step 3: Elimination of incorrect options.
It is not saturated, not homocyclic, and its correct molecular formula is \( \mathrm{C_5H_6O} \), not sulfur-containing.
Step 4: Conclusion.
Therefore, the correct statement is that pyran is heterocyclic with an oxygen atom in the ring.