Whenever I post an answer regarding video, I usually corrected by some other user. Lets see how far I get this time.
everymac.com states the following for a MacBook Air "Core i5" 1.6 13" (Early 2015):
||*Although Apple originally only reported that this model could support a single external display up to 2560x1600, third-parties discovered that it actually could support a 3840x2160 (4K) display, and Apple subsequently revised their official documentation to confirm this, as well.
Apples Technical Specifications states for MacBook Air (13-inch, Early 2015):
Graphics and Video Support
Intel HD Graphics 6000
Dual display and video mirroring: Simultaneously supports full native resolution on the built-in display and up to 3840 by 2160 pixels on an external display, both at millions of colors.
Thunderbolt digital video output
◦ Native Mini DisplayPort output
◦ DVI output using Mini DisplayPort to DVI Adapter (sold separately)
◦ VGA output using Mini DisplayPort to VGA Adapter (sold separately)
◦ Dual-link DVI output using Mini DisplayPort to Dual-Link DVI Adapter (sold separately)
◦ HDMI audio and video output using third-party Mini DisplayPort to HDMI Adapter (sold separately)
According to DisplayPort.org, "4K Ultra HD refers to 3840 x 2160 pixels".
I assume then you would probably what a mini DisplayPort to 4K HDMI adapter (or cable) and monitor with HDMI input and at least 4K resolution.
I believe the fact that the Mac's mini DisplayPort can also do Thunderbolt 2 is not really relevant in this case.