Funeral home will have 4x4 4K HDMI matrix with existing 1080p TVs (possibly being replaced in future)

They want to have a camera in a room to broadcast to TVs.

What type of camera is this? It would be nice if it had HDMI output

Depends on whether you want a fixed or variable focal length lens, whether you want to animate the camera or not. How do you plan on distributing the signal to the multiple TV's? Are you thinking about streaming the services so that distant folks can attend?

Assuming just a fixed lens cam or a pre-set varifocal I would look into Hanwha. Majority of their cameras now have an HDMI output on them.

I've used Avipas and JVC in the past without any issues. If you want to stream over facebook, youtube, etc you will need sother hardware. If you are just showing it on the TVs in the funeral home they will be fine. A lot of decent brands out there. The JVCs are more expensive than the Avipas but definitely do better in low light and give a better picture.

Thanks do you have particular models for me to look at? I think all I would need is zoom at a fixed position

There are at TONS of models bt various manufacturers. Some that come to mind are the JVC KY-PZ100 and Avipas AV-1081 and are near the opposite ends of the price spectrum. Both companies make many other models as do many other companies like PTZO, Sony, Canon, Panasonic, Vaddio and many other players in this arena. Anything with just a zoom is probably just as expensive as a PTZ. Many that are PTZ can be controlled by the web. There are some that can use a remote control and it might be easier for some to just use the remote/joystick instead of a web browser to adjust its position/ zoom. Also, if you want audio make sure the model has a mic or an audio input connection you can attach a mic.

AVer or PTZ Optics would be my choice. Vaddio has great cameras but are a bit costly.