Photosynthesis is not a characteristic of fungi. Most green plants use photosynthesis to obtain their food, but fungi get their food from living, or formerly living, material.
Cellulose in the cell walls of fungi are also not a characteristic of fungi as they are with plants. Instead, the cell walls of fungi are made of chitin, the same material that forms the exoskeletons of arthropods. Fungi may have more in common with animals than they do with plants.
Though fungi can be destructive, they play a vital role in the health of the ecosystem because they break down organic matter. They are also used as food and medicine.