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Results tagged with ct.category-theory
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user 4362
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
10
votes
1
answer
897
views
Category Theory / Topology Question
Let me begin by noting that I know quite little about category theory. So forgive me if the title is too vague, if the question is trivial, and if the question is written poorly.
Let $\mathcal{C}$ a …
- 29.2k
11
votes
1
answer
2k
views
Stacks vs. Groupoids
I'm not an algebraic geometer, but I've been doing a little armchair reading on stacks just to see what all the fuss is about. It appears that stacks are used in algebra in a similar way that groupoi …
- 29.2k
69
votes
7
answers
15k
views
The main theorems of category theory and their applications
This question first arose as I wrote an answer for the question: Is there a nice application of category theory to functional/complex/harmonic analysis?; it can also be regarded as a (hopefully) more …
26
votes
Accepted
'Category-theory'-free areas of pure math, 'category-theory'-loaded areas of applied math
As a (slowly) recovering category-phobe, allow me to suggest that you change the way you think of category theory. Specifically, don't think of category theory as a "theory". A theory in mathematics …
21
votes
Mindset to understand category theory
I think Fong and Spivak's Seven Sketches in Compositionality is the ideal answer to this question. You phrased your question as being about the "mindset" that you need to learn category theory, and i …
28
votes
Is there a nice application of category theory to functional/complex/harmonic analysis?
I've never completely understood what counts as "an application of category theory". With other areas of mathematics an "application" of area A to area B is generally a result which translates a prob …
36
votes
Accepted
Analysis from a categorical perspective
I hesitate to let this out, but there's always this cute little note that I learned from another MO answer (I don't know which one): https://www.maths.ed.ac.uk/~tl/glasgowpssl/banach.pdf. Maybe this …
- 29.2k
30
votes
Why higher category theory?
Here is a fairly naive answer from a non-expert.
If you've studied algebraic topology then you can probably appreciate the philosophy that for the purposes of homotopy theory you should not consider …