That's right: From June 3 to July 2, there'll be a post each day highlighting Teenage Mutant Ninja Turtles canon immigrants. Now, because TMNT canon is a little confusing, it can be hard to tell what counts as a canon immigrant and what doesn't. So for the purposes of this blog, a TMNT canon immigrant is anything (a) from the movies, cartoons, video games, toy lines, or tie-in comic series that later appeared in (b) TMNT volumes 1, 2, or 4 [because they're by the original creators] or TMNT volume 5 [because the original creators are involved, it's the new official continuity, and its goal is to use as much of the diverse TMNT lore as possible].
The Battle Nexus first appeared in the 2003 series in the episode "The Big Brawl, Part 1" (May 2004). It is a dimension that connects such places as Earth and the Triceraton homeworld, and every three years, champions from each area compete in the Battle Nexus Tournament.
The Battle Nexus holds the distinction of being one of the few immigrants to make it into both the Mirage and IDW continuities. Peter Laird had a hand in the 2003 series and was writing volume 4 of the Mirage comics at the same time, so some of the ideas cross-pollinated. The Battle Nexus was first referenced in Teenage Mutant Ninja Turtles #24 (October 2005) and then later actually appears in Teenage Mutant Ninja Turtles #26 (December 2005).
And finally, the Battle Nexus would show up in Teenage Mutant Ninja Turtles Annual 2014 (August 2014) when it's established to replace the bloody tournament that the majority of that story was about. Unfortunately, I can't find a scan of that particular reference.