2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61546We consider basic algebraic constructions associated with an abstract pre-operad, such as a $\smile$-algebra, total composition $\bul$, pre-coboundary operator $\de$, tribraces $\{\cdot,\cdot,\cdot\}$ and tetrabraces $\{\cdot,\cdot,\cdot,\cdot\}$. A derivation deviation of the pre-coboundary operator over the tetrabraces is calculated in terms of the $\smile$-multiplication and tribraces.18 pages, AmSLaTeX, no figuresQuantum AlgebraCategory Theory18D50text