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I agree that to an inexperienced reader, most of your points would be valid. The downside is, it would be too verbose (imagine defining what big R is, for examp

I agree that to an inexperienced reader, most of your points would be valid. The downside is, it would be too verbose (imagine defining what big R is, for example). It being too verbose would stray away a different subset of readers, which arguably is more invested in learning (the number of readers that know what R and a monoid are but not category theory). I think that the best way forward in your case is simply googling terms that the writers took for granted and which you don't understand (a monoid, for example), because the book material is one of the best I've seen on category theory.

CuriousSkeptic 7y ago
While a monoid in abstract algebra is easy enough to understand from Wikipedia. Googling for monoids in the context of category theory could easily land you at nlab I.e https://ncatlab.org/nlab/show/monoid+in+a+monoidal+category https://ncatlab.org/nlab/show/monoid+in+a+monoidal+category I’m not sure that’s helpful to new a learner of the subject. I recall that my personal experience of learning about CT was unnecessarily difficult due to being thrown into a bunch of definitions way to soon. (Which is understandable since there isn’t much else to it.) but I needed to un-learn my preconceptions about what information the theory encodes first, which was rally hard. Understanding that objects and morphisms are really _only_ about composability and _nothing else_ is challenging when your mind desperatly wants to see concrete thing like sets or numbers or what have you in those objects. Definition don’t help much until you can shed that urge. (To new learners I suggest to think of “objects” as the number of dots on domino tiles, or the poles of magnets, they describe where things may, or may not, compose, nothing more. category theory is just about naming patterns and rules of composition) In particular even knowing the existence of monoidal categories is a distraction when getting to grips with how catgories as such generalize and abstracts monoids.
- kidintech 7y ago
  > CT was unnecessarily difficult due to being thrown into a bunch of definitions way to soon I had a similar experience. Luckily, due to reading many definitions of the basic things (such as monoids), I reached a more complete? intuition of the concept if you will. I think that given enough definitions, people will converge to the same intuition of abstract concepts. > To new learners I suggest to think of “objects” as the number of dots on domino tiles, or the poles of magnets, they describe where things may, or may not, compose, nothing more Wouldn't a simpler intuition of circles and arrows be easier?
  - CuriousSkeptic 7y ago
    I meant that as examples of concrete simple things (that aren’t functions, types, sets or any other not fully understood concept) with composition rules that could be modeled in a category. Categories might be drawn using arrows and circles. But that’s just notation.
brohee 7y ago
A glossary as an annex sounds like a way to address this... Big-R and monoid would definitely warrant an entry.
- kidintech 7y ago
  Yep, that seems like an elegant solution.
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CuriousSkeptic 7y ago

While a monoid in abstract algebra is easy enough to understand from Wikipedia. Googling for monoids in the context of category theory could easily land you at nlab I.e https://ncatlab.org/nlab/show/monoid+in+a+monoidal+category https://ncatlab.org/nlab/show/monoid+in+a+monoidal+category I’m not sure that’s helpful to new a learner of the subject. I recall that my personal experience of learning about CT was unnecessarily difficult due to being thrown into a bunch of definitions way to soon. (Which is understandable since there isn’t much else to it.) but I needed to un-learn my preconceptions about what information the theory encodes first, which was rally hard. Understanding that objects and morphisms are really _only_ about composability and _nothing else_ is challenging when your mind desperatly wants to see concrete thing like sets or numbers or what have you in those objects. Definition don’t help much until you can shed that urge. (To new learners I suggest to think of “objects” as the number of dots on domino tiles, or the poles of magnets, they describe where things may, or may not, compose, nothing more. category theory is just about naming patterns and rules of composition) In particular even knowing the existence of monoidal categories is a distraction when getting to grips with how catgories as such generalize and abstracts monoids.

kidintech 7y ago
> CT was unnecessarily difficult due to being thrown into a bunch of definitions way to soon I had a similar experience. Luckily, due to reading many definitions of the basic things (such as monoids), I reached a more complete? intuition of the concept if you will. I think that given enough definitions, people will converge to the same intuition of abstract concepts. > To new learners I suggest to think of “objects” as the number of dots on domino tiles, or the poles of magnets, they describe where things may, or may not, compose, nothing more Wouldn't a simpler intuition of circles and arrows be easier?
- CuriousSkeptic 7y ago
  I meant that as examples of concrete simple things (that aren’t functions, types, sets or any other not fully understood concept) with composition rules that could be modeled in a category. Categories might be drawn using arrows and circles. But that’s just notation.

brohee 7y ago

A glossary as an annex sounds like a way to address this... Big-R and monoid would definitely warrant an entry.

kidintech 7y ago
Yep, that seems like an elegant solution.

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