1
vote
1answer
180 views

Concise definition of subobjects

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, ...
2
votes
1answer
985 views

What is “augmented algebra”?

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. ...
9
votes
2answers
2k views

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 ...
58
votes
18answers
7k views

Can a mathematical definition be wrong?

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 ...
59
votes
23answers
22k views

What are the most misleading alternate definitions in taught mathematics?

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 ...