#categorytheory #math #Https:/
Biomedical and Electrical Engineer with interests in information theory, evolution, genetics, abstract mathematics, microbiology, big history, IndieWeb, mnemonics, and the entertainment industry including: finance, distribution, representation
@RamaKunapuli, because I know you need fun in the spring: Categorical Homotopy Theory by @emilyriehl http:/
#categorytheory
In a Search for a Structure, Part 1: On Entropy. Category theory is the appropriate language for describing entropy.
Mathematics is about ”interesting structures”. What make a structure interesting is an abundance of interesting problems; we study a structure by solving these problems.
The worlds of science, as well as of mathematics itself, is abundant with gems (germs?) of simple beautiful ideas. When and how may such an idea direct you toward beautiful mathematics?
I try to present in this talk a few suggestive examples.
#categorytheory #entropy
Physics, Topology, Logic and Computation: A Rosetta Stone #categorytheory
arXiv:0903.0340 [quant-ph]
In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much like a "cobordism". Similar diagrams can be used to reason about logic, where they represent proofs, and computation, where they represent programs. With the rise of interest in quantum cryptography and quantum computation, it became clear that there is extensive network of analogies between physics, topology, logic and computation. In this expository paper, we make some of these analogies precise using the concept of "closed symmetric monoidal category". We assume no prior knowledge of category theory, proof theory or computer science.
#categorytheory, #physics, #topology
Free textbook: Abstract and Concrete Categories: The Joy of Cats
Abstract and Concrete Categories was published by John Wiley and Sons, Inc, in 1990, and after several reprints, the book has been sold out and unavailable for several years. We now present an improved and corrected version as an open access file. This was made possible due to the return of copyright to the authors, and due to many hours of hard work and the exceptional skill of Christoph Schubert, to whom we wish to express our profound gratitude. The illustrations of Edward Gorey are unfortunately missing in the current version (for copyright reasons), but fortunately additional original illustrations by Marcel Erné, to whom additional special thanks of the authors belong, counterbalance the loss.
Open access includes the right of any reader to copy, store or distribute the book or parts of it freely. (See the GNU Free Documentation License at the end of the text.)
#categorytheory #mathematics #textbook
I came to your article in a terrifically circuitous fashion (via a serendipitous Google Image search), but am so glad that I did. Now it appears I'll end up spending the rest of my day reading all your links and references. I work in areas of information theory and molecular biology and have been filling in my knowledge of mathematics over time. Having just finished up six months of work in Lie groups and algebras, it would appear that category theory is the next sandbox in which I should play. Thanks especially for the textbook references as well as the journal articles!
#categorytheory #mathematics #abstractalgebra #topology