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I suggest the terminology “trivial X” should be reserved for Xs which are zero objects. When the terminal object is not initial, then it’s unjustified to single it out as “the trivial object”.
So I think speaking of the “trivial category” (as this and other entries now do) is not a good idea. Who says this anyways? Google’s first hit after the nLab is proofwiki.org/wiki/Definition:Trivial_Category which says that both the initial as well as the terminal category “can be seen described as trivial”.
Good point. Is there any reference in the literature for Toby Bartels’s definition of a trivial algebra? Toby Bartels wrote the current definition of trivial algebra on September 4, 2010 and did not provide any references at all.
When the terminal object is not initial, then it’s unjustified to single it out as “the trivial object”.
In the case of algebras, there’s an argument that 1 is the “most trivial” algebra, because 0 cannot be an algebra for algebraic structures with constants, whereas 1 is always an algebra for any algebraic structure.
That said, I don’t think there’s much value in having this page (rather than a remark on algebra).
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