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The text discusses composition in the clys Lee category and shows that the classic category is equivalent to the full subcategory of free objects in the island burg more category. It explains that the clys Lee category is the initial object in the category of T inducing a joint situation. In a joint situation FG, there is a unique functor J from the clys Lee category to a category such that J ft equals f and g J equals u T. It further proves that J is full and faithful for arbitrary objects, showing that the home set of morphisms in the clys Lee category from X to X prime can be isomorphic to the home set from FX to FX prime, with J acting on morphisms.
