Which structure in fungi functions as a root system by embedding itself into the material it grows on?

The mycelium is the correct answer, as it serves a role similar to roots in that it permeates the substrate in which the fungi grow. It is a vast network of filaments known as hyphae, which spread throughout the material and increase the surface area for absorption of nutrients and water. This structure allows fungi to efficiently break down organic matter and absorb nutrients, effectively anchoring them into their environment.

In contrast, rhizoids are structures associated with certain plants and some fungi that can anchor the organism, but they are not the primary structure in fungi for nutrient absorption. Hyphae are the individual filament components that make up the mycelium but do not function independently as a root system. Stolons are horizontal connections that allow the fungal organism to spread but do not serve the anchoring or absorptive functions of a root system.

Thus, mycelium is the correct answer, emphasizing its essential role in the lifestyle and nutrient acquisition of fungi.