Fabric Language Kotlin is one of the many Fabric Language adapters for Kotlin. Language adapters let you write mods in programming languages other than pure Java (often but not always JVM-based languages). There are many big Fabric mods which use Kotlin including

Adorn
Inventory Tweaks
AE Additions – ExtraCells2 Fork
Bountiful
DeftuLib
Hex Casting
Industrial Revolution
Inventerio
Kambrik
Lakeside
LibrarianLib
Level Up HP
MirageFairy2023
Ping Wheel
Plethora Peripherals
Roughly Enough Trades
Roughly Enough Loot Tables
RSWires
TerrarianSlimes
Woods and Mires
Zoomify
and many more.

Kotlin is primarily a JVM-based programming language like Groovy or Scala and is in many ways considered a newer Scala (though Scala is still being developed), though it does not only compile to JVM, it can also compile to native or to JavaScript or even its own bytecode format. Fabric Language Kotlin is meant to be used with the JVM variant though.

Kotlin as mentioned before has some in common with Scala and a little in common with Crystal. Kotlin Language is a must-use for many people, many people really like it, while others do not. One issue you have is if you use Kotlin you may have compatibility issues with lesser-known tool chains that you may port your mod too. But if you want to use Kotlin because you prefer it you can use this language adapter. There are reasons to prefer Kotlin if you like some of the features or if you want to also do things like Android development (which has recently started to recommend Kotlin over Java which it had previously). If you use Kotlin it is suggested you use IntelliJ because they are made by the same company and eclipse does not have quite as good of support for it.

For players, you should be able to just install the mod in your mods folder. If you are a developer you will need to take extra steps and requires the user already know a little bit about using Kotlin with Gradle (but Groovy DSL can still be used unless you want Kotlin DSL). FabricMC has a tutorial which can be used with basic instructions about getting started. Fabric Language Kotlin does not rely on any specific version of Minecraft, just on Fabric loader.

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Fabric Language Kotlin Mod