In short
Karyogamy is the fusion of two nuclei into one. In fungi it follows plasmogamy, the fusion of the cytoplasm of two cells.
Sexual reproduction in a fungus has three stages. In plasmogamy, two hyphae join and their cytoplasm mixes, but the nuclei stay separate. In some fungi, such as mushrooms, this gives a cell with two nuclei, called a dikaryon. In karyogamy, the two nuclei fuse, making a diploid nucleus. Meiosis then restores the haploid number and makes spores.
In a mushroom the dikaryotic stage can last a long time, because the two nuclei fuse only later in the gills, inside the basidium. Meiosis then follows and makes four spores.
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