What puts together composites according to Buddhism?

In theravada it is that element which creates that which is created; it creates, therefore it is called the element which creates. As it is thus objectified, it is know as a requisite for other elements so that which forms the formations is classified as formation element forming consciousness as consciousness, formation element forming form as form etc

The classes of past, present & future creating elements are called sankhara aggregate. Sankhara (aggregate) is translated as mental formations or fabrications. Pali discourses explain that fabrications there are intentions, the six classes of intention.

In the Pali texts mind preceeds all created things, it creates them and that which is called mind, consciousness or intellect arises as one thing and ceases as another. Many of the discernable elements are named and known as their coming into play is understood and are named as to their particular function, therefore even tho it is possible to delineate the difference between some elements it would not be possible to take them apart as they are conjoined.

Fabrications "And what are fabrications? These three are fabrications: bodily fabrications, verbal fabrications, mental fabrications. These are called fabrications.

"In-&-out breaths are bodily; these are things tied up with the body. That's why in-&-out breaths are bodily fabrications. Having first directed one's thoughts and made an evaluation, one then breaks out into speech. That's why directed thought & evaluation are verbal fabrications. Perceptions & feelings are mental; these are things tied up with the mind. That's why perceptions & feelings are mental fabrications."

‘Whatever fabrications , bhikkhus, has passed, ceased, changed: the term, label, and description ‘was’ applies to it, not the term ‘is’ or the term ‘will be.’ "And what are fabrications? These six classes of intention — intention with regard to form, intention with regard to sound, intention with regard to smell, intention with regard to taste, intention with regard to tactile sensation, intention with regard to ideas: these are called fabrications. From the origination of contact comes the origination of fabrications. From the cessation of contact comes the cessation of fabrications. And just this noble eightfold path is the path of practice leading to the cessation of fabrications... The fact that pleasure & happiness arises in dependence on fabrications: that is the allure of fabrications. The fact that fabrications are inconstant, stressful, subject to change: that is the drawback of fabrications. The subduing of desire & passion for fabrications, the abandoning of desire & passion for fabrications: that is the escape from fabrications...

“And why, bhikkhus, do you call them fabrications? ‘They fabricate the conditioned,’ bhikkhus, therefore they are called fabrications. Mind precedes fabricated things; Mind directs them, they are mind-made. And what is the conditioned that they fabrications?

They fabricate conditioned form as form; they fabricate conditioned feeling as feeling; they fabricate conditioned perception as perception; they fabricate conditioned fabrications as fabrications; they fabricate conditioned consciousness as consciousness.

‘They fabricate the conditioned,’ bhikkhus, therefore they are called fabrications.

Conditioned Element There are, Ānanda, these two elements: the conditioned element and the unconditioned element. Bhikkhus, there are these three characteristics that define the conditioned. What three? An arising is seen, a vanishing is seen, and its alteration while it persists is seen. These are the three characteristics that define the conditioned. The born, come-to-be, produced, The made, the conditioned, the transient, Conjoined with decay and death, A nest of disease, perishable, Sprung from nutriment and craving's cord — That is not fit to take delight in.

Excerpts from sutta and abhidhamma