Is the new Mac mini compatible with the Apple HD Cinema Display ?
I don't know what's compatible with the HD Display ? My older Mac mini is outdated & only @ Mac OX 10.4
Mac mini 2018 or later
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What specific display? Googling results in this.
Apple Cinema HD Display (23") - Technical Specifications
That monitor has a Apple Display Connector (ADC) that provides all power from the monitor to the display. No Mac Minis had an ADC video output. While there are adopter/converter that can power an ADC monitor they are expensive like>$200, so not worth it.
If the display has an DVI or mini displayport input they adopters are reasonable.