Higher category theory tells us that it is a bad idea to identify isomorphic things. Rather, the isomorphism should belong to some additional data. Also, categorification tells us that one should, ...
Really sorry for this question, but googling for some time did not help me. I was trying to understand the meaning of the following phrase: Let B be an augmented algebra over a semi-simple algebra T. ...
What are examples of theorems which were once “valid”, then became “invalid” as standard definitions shifted?
That is, results established by correct proofs within some framework, yet the manner in which their author or the general mathematical community at the time would describe these results would, in ...
This question originates from a bit of history. In the first paper on quantum Turing machines, the authors left a key uniformity condition out of their definition. Three mathematicians subsequently ...
I suppose this question can be interpreted in two ways. It is often the case that two or more equivalent (but not necessarily semantically equivalent) definitions of the same idea/object are used in ...