how do i connect iMac (27-inch, Late 2013) to mac mini in order to use my imac as a monitor

You need this and a Thunderbolt 1/2 cable:

https://www.apple.com/shop/product/MMEL2AM/A/thunderbolt-3-usb-c-to-thunderbolt-2-adapter?fnode=aed7e48b4814c08c0bf20a3278ce7b8059c91771a7690843a883713d19f141d265441a31a7014793236bce747dba95b4a19cc1e99f6331f1b6a2c87dbebacc26f29f35d6e8dbdf08136d172a2f81024eadcd53728b7e7329ec22f78ed181a2300ba153c11de5791843011f1e1223c775

Connecting with HDMI is not an option in any way shape for form.

Hello, superderv.

Here are the rules for Target Display mode on iMac:

click> Use your iMac as a display with target display mode - Apple Support

Target display mode is a feature that was available only with certain older iMac models.

Only the following older iMac models can be used as an external display when plugged into another older Mac model:

• iMac models introduced in 2011, 2012, 2013, and mid 2014 using Thunderbolt or Thunderbolt 2 cable.
• 24-inch and 27-inch iMac models introduced in 2009 and 2010 using Mini DisplayPort cable.
• The intended target iMac must be running macOS 10.13 High Sierra or earlier; it does not work with macOS 10.14 Mojave or later, or with Boot Camp and Windows.*
• Retina display iMacs won’t work as target displays.

• In all cases the source Mac that you're connecting FROM must have been introduced in 2019 or earlier and have macOS 10.15 Catalina or earlier installed.

superderv wrote:

Hi thanks for that p- the online advice seems to think that one can connect the thunderbolt 3 on mac mini to hdmi on imac (when using imac as a display) but i take your point that it may not work - thanks for the url, that item is an adapter - it's actually a t2 to t3 cable i need, not adapter - the adapter is male and female, i assume i need male and male to insert into the female ports on the mac mini and imac... so i was looking for a male > male cable, rather than an adapter, if you get me.

You need the adapter as no such cable exists.

I spent a long time trying to find one to connect my M1 MacBook Air to my 27" Apple Thunderbolt Display.

There is no other way than using the adapter and a Thunderbolt 1/2 cable.

superderv wrote:

o dear, it looks like i can't buy a Thunderbolt 2 to Thunderbolt 2 (both male) cable from apple... ouch

The adapter's USB-C connector plugs into the Mini Thunderbolt port.

The Thunderbolt cables are male at both ends. One end plugs into the

adapter's female Thunderbolt 2 port and the other end plugs into the back

the back of the iMac.

Apple does sell a Thunderbolt cable (that also supports Thunderbolt 2).

https://www.apple.com/shop/product/MD862LL/A/apple-thunderbolt-cable-05-m

thanks very much for that, i was unable to find a t2 cable when simply browsing the accessories: https://www.apple.com/shop/mac/accessories/power-cables. Much apporeciated.