If cats can be a carrier all this social distancing is for naught. It is known that the environment of Covid-19 patients can be very contaminated. Pets living with infected people are highly exposed to the virus. So far there are only 3 known cases (2 dogs in Hong Kong and 1 cat in Belgium) where the pet has been infected by humans. The dogs showed no disease symptoms and the cat had transient respiratory and digestive disorders. There is no evidence to date that the virus is being transmitted from pets to humans or other pets. Although it is suspected that the virus that causes Covid-19 in humans originally came from wild animals, it has since adapted to humans ("humanized" virus).
Nevertheless, it is strongly recommended to keep applying the classic hygiene rules (avoid close contact with your animal, especially if you are sick, wash your hands after touching an animal, do not let the animal lick your face). This is on the one hand to prevent that you would transmit the virus to your pet and to prevent your pet from becoming a carrier and elimination of the virus as a result of an environmental contamination.
Although it is suspected that the virus that causes Covid-19 in humans originally came from wild animals, it has since adapted to humans ("humanized" virus). The Covid-19 virus shows a lot of sequence homology to a bat coronavirus. I would argue that the virus is not humanized yet, because as microorganisms humanize, they become less virulent. It is not conducive to pathogen survival to kill its host.