Controlling Elgato Keylight Air via Apple Home

This is how you can control the Elgato Keylight Air over Apple's Home.app:

Elgato has no native support for HomeKit, so you will need to have Homebridge installed, and the homebridge-http-light-bulb plugin.

After you have Homebridge and homebridge-http-light-bulb up and running,
add this in the accessories section of your Homebridge config:

{
  "accessory": "HTTP-LIGHTBULB",
  "name": "Elgato Keylight Air",
  "debug": false,
  "onUrl": {
    "url": "http://192.168.1.93:9123/elgato/lights",
    "method": "PUT",
    "body": "{\"numberOfLights\":1,\"lights\":[{\"on\":1}]}"
  },
  "offUrl": {
    "url": "http://192.168.1.93:9123/elgato/lights",
    "method": "PUT",
    "body": "{\"numberOfLights\":1, \"lights\":[{\"on\":0}]}"
  },
  "statusUrl": "http://192.168.1.93:9123/elgato/lights",
  "statusPattern": "\"on\":1",
  "brightness": {
    "statusUrl": "http://192.168.1.93:9123/elgato/lights",
    "statusPattern": "\"brightness\":(\\d*)",
    "setUrl": {
      "url": "http://192.168.1.93:9123/elgato/lights",
      "method": "PUT",
      "body": "{\"numberOfLights\":1, \"lights\":[{\"brightness\":%s }]}"
    }
  },
  "colorTemperature": {
    "statusUrl": "http://192.168.1.93:9123/elgato/lights",
    "statusPattern": "\"temperature\":(\\d*)",
    "unit": "mired",
    "minValue": 143,
    "maxValue": 344,
    "setUrl": {
      "url": "http://192.168.1.93:9123/elgato/lights",
      "method": "PUT",
      "body": "{\"numberOfLights\":1,\"lights\":[{\"temperature\": %s }]}"
    }
  }
}

Save it, and voila!