gistfile1.js

/* category.js */
var mongoose = require('mongoose')
  , Schema   = mongoose.Schema
  , ObjectId = Schema.ObjectId;

var Category = new Schema({
...
});

Category.statics.foobar = function() {
 ...
}

module.exports = mongoose.model('Category', Category);



/* photo.js */
var mongoose = require('mongoose')
  , Schema   = mongoose.Schema
  , ObjectId = Schema.ObjectId
  , Category = require('./category'); //defined here

var Photo = new Schema({
...
});

  Photo.statics.getRandomFromCat = function(category_id, cb) {
    console.log("getRandomFromCat",category_id);
    if(category_id) {
      Category.findById(category_id, function(err, cat) {
        if(err) throw err;
        //....
      }
    } else { 
        //....
    }
  });

module.exports = mongoose.model('User', User);

TypeError: Object function model() {
Model.apply(this, arguments);
} has no method 'getById'