Is the coyote a cat

Coyotes are predators. Coyotes are also meat eaters. A coyote will eat a cat if they hunt and catch one.
YES - if coyotes are in the area, cats are at high risk of being eaten. They are a regular part of their diet, according to studies.

"Coyotes regularly feed on outdoor cats, according to a scientific study, Observations of Coyote-Cat Interactions by Shannon Grubbs of the University of Arizona and Paul Krausman of the University of Montana published in the Journal of Wildlife Management. The researchers tracked coyotes in Tucson, Arizona and observed 36 coyote-cat interactions, of which 19 resulted in coyotes killing cats.

Other studies have found that approximately 13% of a coyote's diet consists of cats. However, during this study, in the 45 instances when coyotes were observed feeding, 42% of the meals were cats. The researchers concluded that any cat outside is vulnerable to coyote attack, and recommended that cat owners keep their cats indoors"
Yes they do. KEEP YOUR CAT INSIDE AT ALL COSTS. Try calling local animal control they will try and catch it if you live in a more populated area they will not set any type of traps like box traps, foot traps, and stakes due to pets and children. But if you live in a rural area they will.