Yeast is a fungus, reason:
This is often an adaptation to living in a liquid medium of high osmotic pressure.
This usually means media with a high sugar content, such as is found in the nectaries of flowers or on the surface of fruits, where if they present the least possible surface area (as close to spherical as possible), it makes it easier for them to control the movement of dissolved substances in and out of their cells.
Also, the cell wall of the yeast of the yeast is chitinous as found in almost all fungi.
During unfavourable conditions, for example, when there is limited nutrient, a diploid yeast cell will form four haploid spores encased in a protective outer layer called the ascus.
Therefore, because of the formation of the ascus like bodies having haploid ascospores, yeasts have been placed in the ascomycetes class of the kingdom fungi.