Category Theory for the Sciences PDF/EPUB Ý for the

Category Theory for the Sciences [PDF / EPUB] Category Theory for the Sciences An introduction to category theory as a rigorous flexible and coherent modeling language that can be used across the sciencesCategory theory was invented in the s to unify and synthesize different are An introduction to category theory as for the eBook ✓ a rigorous flexible and coherent modeling language that can be used across the sciencesCategory theory was invented in the s to unify and synthesize different areas in mathematics and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics This book shows that category theory can be useful outside of mathematics as a rigorous flexible and coherent modeling language throughout the sciences Information is inherently dynamic the same ideas can be organized and reorganized in countless ways and the ability to translate between such organizational Category Theory Epub / structures is becoming increasingly important in the sciences Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplinesWritten in an engaging and straightforward style and assuming little background in mathematics the book is rigorous but accessible to non mathematicians Using databases as an entry to category theory it begins with sets and functions then introduces the reader to notions that are fundamental in mathematics monoids groups orders and graphs categories in disguise After explaining the big three concepts of category theory categories functors and natural transformations the book covers other Theory for the Epub Û topics including limits colimits functor categories sheaves monads and operads The book explains category theory by examples and exercises rather than focusing on theorems and proofs It includes than exercises with solutions Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation neuroscience and physics.

13 thoughts on “Category Theory for the Sciences

  1. says:

    I decided that I needed a formal category theory background when trying to understand typeclasses in Haskell This book perfectly serves the aim, introducing the theory in a formal yet not too abstract way The application to databases and ologs is nice.The book has a formal structure of a mathematical text definitions, propositions, theorems, however often without a proof and a lot of examples.Has a minor drawback though, namely a relatively high density of typos, but I guess it s a common first edition symptom.

  2. says:

    Das Buch zeigt auf, wie das Konzept der Kategorien Theorie in der wissenschaftlichen Praxis nutzbar gemacht werden kann, und bietet damit eine wichtige Erweiterung des Instrumentariums der wissenschaftlichen Arbeit.

  3. says:

    A very accessible and informative book on broad applications of category theory Especially useful in information technology modelling

  4. says:

    Pros Has lots of examples questions with solutions, which help you clearly understand the concepts being discussed, Spivak builds up concepts gradually with lots of worked out examples, Requires little by way of mathematical background Very suitable for non mathematicians or those with basic mathematical background An early version is available online in PDF format, so you can evaluate before buying The book contains solutions after every exercise, not so for the PDF.Cons Much of the early part of the book is motivated by ologs, which I feel have doubtful utility in practical science I feel this detracts from the overall presentation The book takes a long time to actually introduce Categories, because Spivak takes the time to introduce mathematical background However, this forces the reader wade through a lot of material, which is likely unfamiliar to his target audience and I feel is less useful in actually understanding Category theory Overall, I found this bottom up pedagogical approach makes it quite hard to see the forest broad ideas top down, introducing categories almost immediately then examples to flesh out the concepts It has a far abstract and intuitive flavor in its presentation compared to Spivak, which is what I like most about it However, it is also much denser than Spivak, and is a far challenging read, but should still be accessible to anyone with first year college level exposure to abstract algebra.

  5. says:

    David Spivak is a welcome new breed of MIT lecturer whose passion is to motivate, engage, and facilitate a students learning of a subject.Its predecessors are Category Theory for Computer Scientists Barr A First Introduction to Categories Lawvere Category Theory Awodey This book is a Rosetta Stone for understanding the forthcoming new applications of Category Theory to real world issues such as the foundations of computer science e.g., Algebraic Theory of Machines Jack Rhodes and Ken Khon and physics e.g., John Baez.Where was Spivak when one first encountered the new and ethereal Category Theory in the late 1950 s under Dan Kan, Warren Ambrose, andSerge Lang Closest comparison would be BUD S training.And let us not forget the esteemed George Whitehead classes e.g Elements of Homotopy Theorywhich was based on his lectures Enter the class room start writing as fast as possible on the blackboard mimicking tap dancing squirrels, andwhen reaching the end of the blackboards erasing the first board Carpal Tunnel Syndrome for the few survives of his course.As with Barr Topos Theory Dover and Sketches of an Elephant are the ultimate injoyous reading for the mathematically deranged who cannot get enough.Only one kvetch The printing of the text is so light that one wonders if MIT Press had run out of toner, making reading a chore for older readers.In contrast, Norbert Wiener s Cybernetics 2, 1960 is still readable because real ink was used.In conclusion Spivak s book is a joy and an important gateway for a scientist of the new emerging fields.

  6. says:

    Phenomenal book I was looking for a good introduction to category theory for non mathematicians and this definitely hits the mark It starts out very accessible with its use of ontology logs ologs but subsequently gets very mathematical and rigorous, so you ll definitely need some degree of mathematical maturity to appreciate this A good background in proofs set theory should suffice I would recommend Book of Proof by Richard Hammack as a prequel to this book This work covers a lot of interesting ground including set theory, topology, and simplicial complexes.

  7. says:

    This will be short and to the point, rather different from Mr Spivak s book First, I think it is a very good book if you want to see why category theory is useful in computer science It is not a very good book if you want to learn category theory in general, because it is CLUTTERED with too much, well, clutter, between the actual definitions and theorems But there are flashes of brilliance in the exposition and it is probably worth the slog through the clutter A worthwhile effort And I agree with another reviewer that ologs are not worth all the space Spivak gives them I think they really add nothing much and might better be a quick aside in the section on databases.

  8. says:

    A little hard to get through at first, as the descriptions of his fundamental concept, ologs, was both wordy and a bit obtuse But htis is ground breaking in its relationship to the use in computation and that is a big deal By itself it may not be sufficient to grasp all the essentials of category theory and thus Suanders MacLane s Mathematics Form and Function is still the best overall overview

  9. says:

    Arrived promptly, clean and intact.

  10. says:

    Been teaching a lunch time course to my colleagues from this Really sharpens your thinking and helps you find fuzziness, ambiguity, and errors just about everywhere you look.

  11. says:

    This book is one of kind, the only one for readers of none mathematical background It of course still takes quite an effort to learn CT from this book I have a Ph D in engineering and had some advanced algebraic and analytic math courses during my college years So far I only understand the very basic part of the CT The higher category and natural transformation part are still out of my reach I won t blame to author for that I don t have the complete prerequisite I hope some day I will get to it.Despite of that, I have benefited a lot from the learning in my current professional endeavor It helps me sort out the complex domain problems clearly I hope there is a better way of complaining the math, but it may be something not at attainable.

  12. says:

    Best Book on the market for Category Theory Best Author.

  13. says:

    too theoretical for the general public Probably there is practical applications, but was imposible to detect them

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