21–23 of 23 posts
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> it is just so hard to read unfamiliar mathematics I have completely given up on trying to learn anything about math from Wikipedia. It’s been overrun by mathematicians apparently catering to other mathematicians and that’s not the point of an encyclopedia. It’s hostile and pointless. If you want a technically correct site make your own.
It appears that they have.
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> I would like to learn category theory properly one day, at least to that kind of "advance undergraduate" level she mentions. As someone who tried to learn category theory, and then did a mathematics degree, I think anyone who wants to properly learn category theory would benefit greatly from learning the surrounding mathematics first. The nontrivial examples in category theory come from group theory, ring theory, l…
I should have mentioned in my post that I have an applied math masters and a solid amount of analysis and linear algebra with some group theory, set theory, and a smattering of topology (although no algebraic topology). So, I'm not coming to this with nothing, although I don't have the very deep well of abstract algebra training that a pure mathematician coming to category theory would have. Although, it feels like c…
It's a crisp, slim book, presenting topology categorically (so the title is appropriate). It both deepens the undergraduate-level understanding of topology and serves as an extended example of how category theory is actually used to clarify the conceptual structure of a mathematical field, so it's a way to see how the flesh is put on the bare bones of the categorical concepts.
It's also available for free online:
Earlier quoted context omitted.
I should have mentioned in my post that I have an applied math masters and a solid amount of analysis and linear algebra with some group theory, set theory, and a smattering of topology (although no algebraic topology). So, I'm not coming to this with nothing, although I don't have the very deep well of abstract algebra training that a pure mathematician coming to category theory would have. Although, it feels like c…
You could take a look at Topology: A Categorical Approach by Bradley, Bryson and Terilla. It's a crisp, slim book, presenting topology categorically (so the title is appropriate). It both deepens the undergraduate-level understanding of topology and serves as an extended example of how category theory is actually used to clarify the conceptual structure of a mathematical field, so it's a way to see how the flesh is p…