Composer is framework-agnostic: it does not require jQuery, Mootools, or any other framework to function (however, to support older versions of IE, Mootools is reccommended). As of version 1.1.0, Composer’s only external dependency is History.js (and as of 1.2.0, Composer uses morhpdom for its optional xdom feature).
For the curious, read about the differences between Composer and Backbone.
Also see apps using Composer in production »
Composer’s router requires History.js to function properly. Composer’s xdom system requires some form of DOM diffing/patching library (morphdom is the supported default, although you can provide your own).
Composer is tested on recent versions of Firefox, Chrome, Safari, and IE >= 6. Note that IE 6-9 support is dependent on Mootools being present (and will not necessarily be supported in the future). For now, all tests pass in all major browsers.