Looping animation

What Mylenium said!

You'd need to export it as a gif rather than a video file and make sure that wherever you're posting on it plays gifs on a loop. I feel like most platforms automatically loop gifs so you should be good! If you're curious, there are some expressions that will help you loop your keyframed animations without having to copy/paste all your frames. Check out this youtube tutorial for tips! It's 90 seconds.

This has (mostly) nothing to do with AE. This is more or less up to whatever media player software or hardware you use to view the output and their settings, sometimes in conjunction with setting the proper repeat flags like in the GIF format. Of course you can loop stuff in AE using time-remapping and in the footage interpretation, but this will inevitably multiply render times by the same amount and you may then run into all sorts of issues with file size limits, potential quality problems, audio getting out of sync, humungous upload sizes and so on. Typically people will only "loop" stuff around five to ten times in AE if at all and then rely on the technical repeating in the players. Of course this is dependent on the content. Shorter clips benefit from more loops to disguise jumps when the player starts over, longer clips require fewer repetitions or noen at all.

Mylenium