This is a new topic on the algebraic foundations of mathematics.

a. Universal (or general) algebra : is defined as the (meta) mathematical study of general theories of algebraic structures rather than the study of specific cases, or models of algebraic structures.

b. Various, specifically selected algebraic structures, such as :

1. Boolean algebra
2. Logic lattice algebras or many-valued (MV) logic algebras
3. quantum logic algebras
4. quantum operator algebras ( such as : involution, *-algebras, or -algebras, von Neumann algebras, JB- and JL- algebras, Poisson and - or C*- algebras,
5. Algebra over a set
6. sigma-algebra and T-algebras of monads
7. K-algebras
8. group algebras
9. graphs generated by free groups
10. groupoid algebras and Groupoid -convolution algebras
11. hypergraphs generated by free groupoids
12. Double algebras
13. Index of algebras
14. categorical algebra
15. F-algebra/coalgebra in category theory
16. category of categories as a foundation for mathematics: Functor Categories and 2-category
17. Index of category theory
18. super-categories and topological `supercategories'
19. higher dimensional algebras (HDA) –such as: algebroids, double algebroids, categorical algebroids, double groupoid convolution algebroids, groupoid -convolution algebroids, etc., and Supercategorical algebras (SA) as concrete interpretations of the theory of elementary abstract supercategories (ETAS)
20. Index of supercategories
21. Index of categories
22. Index of HDA

Remark The last items of HDA and SA are more precisely understood in the context of, or as generalizations/ extensions of, universal algebras.

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