Tassels belong on corn. Catkins grow on chestnuts!
Some catkins don't have anthers or pollen. Many folks believe no chestnuts are self-compatible (require more than one variety for pollination), but I'm quite certain that is not correct based on my experiences, including witnessing some solitary trees with heavy crops. The stigmas are part of the separate flower that appears to be a small chestnut and are born on the same new growth. I'm probably 2-3 weeks away before flowers here.