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Category Archives: math
Readers wanted!
tl;dr: Read a draft of my thesis and send me your feedback by September 9! Over the past year I’ve had several people say things along the lines of, “let me know if you want me to read through your … Continue reading
Posted in category theory, combinatorics, diagrams, grad school, math, species, writing
Tagged dissertation, feedback, readers, species, thesis
15 Comments
Anafunctors
This is part four in a series of posts on avoiding the axiom of choice (part one, part two, part three). In my previous post, we considered the “Axiom of Protoequivalence”—that is, the statement that every fully faithful, essentially surjective … Continue reading
Posted in category theory, math, species
Tagged AC, anafunctor, axiom of choice, category, constructive, equivalence, functor, isomorphism, theory, types, unique
2 Comments
AC and equivalence of categories
This is part three in a series of posts on avoiding the axiom of choice (part one, part two). In my previous post, I explained one place where the axiom of choice often shows up in category theory, namely, when … Continue reading
Posted in category theory, math, species
Tagged AC, axiom of choice, category, constructive, equivalence, functor, isomorphism, theory, types, unique
5 Comments
Unique isomorphism and generalized “the”
This is part two in a series of posts on avoiding the axiom of choice; you can read part one here. In category theory, one is typically interested in specifying objects only up to unique isomorphism. In fact, definitions which … Continue reading
Posted in category theory, math, species
Tagged AC, axiom of choice, category, constructive, functor, isomorphism, theory, types, unique
8 Comments
Avoiding the axiom of choice, part I
I’m hard at work on my dissertation, and plan to get back to doing a bit of blogging based on stuff I’m writing and thinking about, as a way of forcing myself to explain things clearly and to potentially get … Continue reading
Posted in category theory, math, species
Tagged AC, axiom of choice, category, constructive, theory, types
17 Comments
Catsters guide
tl;dr: http://byorgey.wordpress.com/catstersguide2/ In an attempt to solidify and extend my knowledge of category theory, I have been working my way through the excellent series of category theory lectures posted on Youtube by Eugenia Cheng and Simon Willerton, aka the Catsters. … Continue reading
Random binary trees with a sizelimited critical Boltzmann sampler
Today I’d like to talk about generating random trees. First, some imports and such (this post is literate Haskell). > {# LANGUAGE GeneralizedNewtypeDeriving #} > > module BoltzmannTrees where > > import Control.Applicative > import Control.Arrow ((&&&)) > import Control.Lens … Continue reading
Posted in combinatorics, haskell, math, species
Tagged Boltzmann, generation, QuickCheck, random, sampler, tree
7 Comments