The question is in the title. In order to give a bit more backround about the question, one knows that their are several different notions of an algebraic object. One approach is that of Lavere and his algebraic theories. One may also talk about monads. Another approach is an operadic/prop type approach. Yet another way to define an algebraic object is to use sketches of various types. Their may be other approaches that have not been enumerated. My understanding is that all of the things we would like to consider algebraic are not covered by one of these approaches. So this is where the question in the title comes from. Is their a context where all of the things we would like to consider algebraic fit into the aforementioned context? (of course I may be mistaken)
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closed as not a real question by Franz Lemmermeyer, Ryan Budney, Dan Petersen, David Roberts, Harry Gindi Jun 21 '11 at 8:17It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question. 

