Should I not being using HDMI with 2014 mac mini for 2560x1440 monitor?

The Thunderbolt port should allow a higher resolution option, as the

output specifications would be available with the computer information.

You'd need to acquire the correct adapter cable(s) and perhaps another

for audio, when most Macs don't share audio with video output.

Good luck! 🙂

What model Mini?

The latest, the late 2014 Mini supports:

Support for up to two displays at 2560 by 1600 pixels, 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 video output

• Support for 1080p resolution at up to 60Hz
• Support for 3840-by-2160 resolution at 30Hz
• Support for 4096-by-2160 resolution at 24Hz

DVI output using HDMI to DVI Adapter (sold separately)

Thunderbolt/mini display port only still supports only 30 Hz max with 4K monitor.

See:

Using 4K displays and Ultra HD TVs with your Mac - Apple Support

Previous Mac Mini do not support 4k and only max of 1080p from HDMI

Thanks, lllaass for the clarification, I'd not performed detailed search for this info

and though I have the similar (Late 2012) Mini quad-core, have simple 20-inch

DVI Aluminum Apple Cinema display. It was an upgrade for my G4 Mini 1.5GHz

& now is in use with this Q-C model since January; the old Mini has a samsung.

(PS: iTried to reply to your invisible post, but it wasn't visible except in the inbox.)

So someday after the lottery finds me amid my alias incognito status, I'll upgrade more...😝

Correct. A mini displayport/displayport connection is best