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I'd say that you can safely ignore CT until you find the need or desire to learn more. The field is still very young and it probably shines most within pure mat

I'd say that you can safely ignore CT until you find the need or desire to learn more. The field is still very young and it probably shines most within pure mathematics, for now at least. I think of CT as the study of "composability" in its purest form. Mathematicians are finding that this language is really good at translating domain-specific knowledge between disparate fields, not unlike the babelfish from the Hitchhiker's Guide. FWIW, some researchers are apparently finding interesting applications in the development of biological models. John Baez has talked about applications in this direction via control theory [0]. [0]:https://classes.golem.ph.utexas.edu/category/2015/04/categories_in_control.html https://classes.golem.ph.utexas.edu/category/2015/04/categor...

mtzet 8y ago
Let me expand a bit on the origin of category theory in mathematics. Mathematics is most commonly described in the language of set theory, where objects are constructed from basic building blocks to create bigger blocks. This is much in the same way as algorithms are described in something concrete, say a programming language. At some point, certain high-level constructs started to appear, where the same high-level behaviour was exhibited in otherwise completely disconnected fields. Explaining what is going on then started to become messy, for example take following quote from Hatcher's Algebraic Topology concerning covering spaces: "This is often called the Galois correspondence because of its surprising similarity to another basic correspondencein the purely algebraic subject of Galois theory". The problem is that in order to understand this, the reader has to understand two fields which are not at all connected and furthermore, the relationship looks nothing alike in the language of set theory. Category theory was invented as a formal language which could describe such high-level behaviour. In this language this language we would could now say that there is an "contravariant equivalence of categories", which helps if you've seen it before and doesn't help at all if you haven't. So category theory is massively useful in understanding the similarities between fields, and can be used to transfer understanding from one field to another. It it also useful for understanding more abstract fields where the intuition must be gained by analogy with something more concrete. It doesn't do much in itself, and I don't think it makes much sense to study the mathematical aspects of category theory without any good examples to apply it to. What does that have to do with engineering? I'm not expert here, and haven't yet read the linked book, but one could hope that certain similarities could be described in terms of this new language. Then concepts which now only live on as the expert experience of working practitioners, might be written down and hence taught directly rather than indirectly. One could hope that certain problems have common solutions which can be re-used across fields.
YorkshireSeason 8y ago
Category theory studies the composition of (things that look like) functions. So each thing has a domain, and a codomain, and if we compose A --f--> B with B --g--> C then the intermediate B goes away. This doesn't sit nicely with how parallel composition works, e.g. If I talk to Google, that doesn't prevent you from talking to Google. That's the essence of why category theory works nicely with pure functional programming, but beyond that simply fails to be useful. In particular, there has been virtually no progress in useful categorical models of parallel computation.
- eru 8y ago
  What about eg http://lambda-the-ultimate.org/node/4823 http://lambda-the-ultimate.org/node/4823 ?
  - YorkshireSeason 8y ago
    I don't see much / any category theory in the two papers linked. So I'm not sure what to say.

mtzet 8y ago

Let me expand a bit on the origin of category theory in mathematics. Mathematics is most commonly described in the language of set theory, where objects are constructed from basic building blocks to create bigger blocks. This is much in the same way as algorithms are described in something concrete, say a programming language. At some point, certain high-level constructs started to appear, where the same high-level behaviour was exhibited in otherwise completely disconnected fields. Explaining what is going on then started to become messy, for example take following quote from Hatcher's Algebraic Topology concerning covering spaces: "This is often called the Galois correspondence because of its surprising similarity to another basic correspondencein the purely algebraic subject of Galois theory". The problem is that in order to understand this, the reader has to understand two fields which are not at all connected and furthermore, the relationship looks nothing alike in the language of set theory. Category theory was invented as a formal language which could describe such high-level behaviour. In this language this language we would could now say that there is an "contravariant equivalence of categories", which helps if you've seen it before and doesn't help at all if you haven't. So category theory is massively useful in understanding the similarities between fields, and can be used to transfer understanding from one field to another. It it also useful for understanding more abstract fields where the intuition must be gained by analogy with something more concrete. It doesn't do much in itself, and I don't think it makes much sense to study the mathematical aspects of category theory without any good examples to apply it to. What does that have to do with engineering? I'm not expert here, and haven't yet read the linked book, but one could hope that certain similarities could be described in terms of this new language. Then concepts which now only live on as the expert experience of working practitioners, might be written down and hence taught directly rather than indirectly. One could hope that certain problems have common solutions which can be re-used across fields.

YorkshireSeason 8y ago

Category theory studies the composition of (things that look like) functions. So each thing has a domain, and a codomain, and if we compose A --f--> B with B --g--> C then the intermediate B goes away. This doesn't sit nicely with how parallel composition works, e.g. If I talk to Google, that doesn't prevent you from talking to Google. That's the essence of why category theory works nicely with pure functional programming, but beyond that simply fails to be useful. In particular, there has been virtually no progress in useful categorical models of parallel computation.

eru 8y ago
What about eg http://lambda-the-ultimate.org/node/4823 http://lambda-the-ultimate.org/node/4823 ?
- YorkshireSeason 8y ago
  I don't see much / any category theory in the two papers linked. So I'm not sure what to say.