Audio out to hdmi in?

I have an old digital audio tape recorder and want to capture audio signal from a DAT-tape to my computer. The recorder has digital coaxial audio output, AES/EBU output and optical audio output. My laptop has an hdmi plug. Can I use the hdmi on my laptop as an input to capture the digital or optical audio signal?

Think I found what I need: https://www.walmart.com/ip/Component-Vi ... 10&veh=aff

Don't fall for these cheap sort of video devices, as this is a video converter, it needs also a video signal.
There are digital to analog adapters, even cheaper, that do convert. coaxial/optical to analog and visa versa.
do a google for "digital to analog converter" in your (webshop) region, and you will find plenty in all budget ranges.

Better is to search for a USB version, so it will not use your internal audio interface of your PC/Laptop

I have an old digital audio tape recorder and want to capture audio signal from a DAT-tape to my computer. The recorder has digital coaxial audio output, AES/EBU output and optical audio output. My laptop has an hdmi plug. Can I use the hdmi on my laptop as an input to capture the digital or optical audio signal?

Something like FiiOD3 (D03K) DAC is better.

Some PC's or laptop's have this allready as an option on their sound card, if you have a combined Line in Optical in, (3.5mm optical adapter) you would be ready, and you need only a coaxial to optical converter, if not you need an audio interface like people in the music industry use, the prices may vary a lot in this sector, but they are really affordable ones,
and for all sample and bit rates. like i said, you should want to convert to USB in your case, or use a combination of converters if needed.
Dolby surround sets Home theatre, receivers/amplifiers, have also digital/toslink/coaxial input, but i guess they have no USB output, Depending if you still want to use the DAT recorder for recording in the future, you might want to buy a (rack) digital recorder, you will have digital input this way, record to SD (flash) cards, HDD, network, or even writable cd-r's in wav, or mp3 format.
It al depends if you need this hardware also in the near future for your work (flow)