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The study of algebraic structures and properties applying to large classes of such structures. For example, ideas from group theory and ring theory are extended and considered for structures with other signatures (systems of basic or fundamental operations).
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Ternary associative multiplication
In this answer Brian M. Scott describes the following generalization of a binary associative multiplication to a ternary one: it is a function $$[\cdot,\cdot,\cdot] : G\times G \times G \to G$$ such t …
4
votes
The groupoid of algebraic expressions and proofs
I don't have any direct reference for the notion that you are describing, however the notions of $E_n$-algebras and (topological) operads are very close. Firstly, you should note that you need equalit …