Mathematical Structures

All models listed below are the unique lexicographically least member of their isomorphism class.

1. Bands
2. Bands with zero
3. Binars
4. Binars with zero
5. Cancellative binars
6. Cancellative commutative binars
7. Cancellative commutative partial binars
8. Cancellative commutative partial monoids
9. Cancellative commutative partial semigroups
10. Cancellative conjugative partial binars
11. Cancellative conjugative partial monoids
12. Cancellative conjugative partial semigroups
13. Cancellative partial binars
14. Cancellative partial monoids
15. Cancellative partial semigroups
16. Commutative binars
17. Commutative integral lattice-ordered monoids
18. Commutative loops
19. Commutative moniods
20. Commutative partial binars
21. Commutative partial moniods
22. Commutative partial semigroups
23. Commutative semigroups
24. Commutative semirings
25. Commutative idempotent integral semirings with zero
26. Commutative idempotent semirings with zero and one
27. Commutative idempotent semirings
28. Commutative multiplicatively and additively idempotent semirings
29. Commutative multiplicatively and additively idempotent semirings with zero
30. Commutative multiplicatively and additively idempotent semirings with zero and one
31. G-sets
32. Generalized effect algebras
33. Generalized orthoalgebras
34. Idempotent integral semirings with zero
35. Idempotent integral semirings
36. Idempotent semirings
37. Idempotent semirings with zero = Quantales
38. Integral lattice-ordered monoids
39. Integral residuated lattices
40. Join-semilattices
41. Lattices
42. Lattice-ordered monoids
43. Lattice-ordered semigroups
44. Loops
45. Moniods
46. Moniods with zero
47. Partial binars
48. Partial monoids
49. Partial semigroups
50. Partial unars
51. Quasigroups
52. Residuated lattices
53. Semigroups
54. Semigroups with zero
55. Semirings
56. Semilattices
57. Separation algebras
58. Unital bands
59. Unital bands with zero
60. Unars

• Unary clones on {0,1} (6)
• Unary strong clones on {0,1} (9)
• Unary structural clones on {0,1} (17, 22)
• Unary partial clones on {0,1} (33, 43)

• Unary clones on {0,1,2} (699)

• Binary clones on {0,1} (26)
• Binary strong clones on {0,1} (takes 2 minutes to load) (412)
• Binary structural clones on {0,1} (takes 5 minutes to load) (1693, 1767)