Category Archives: math

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

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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

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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

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Catsters guide

tl;dr: https://byorgey.wordpress.com/catsters-guide-2/ 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

Posted in haskell, math, teaching | Tagged | 2 Comments

Random binary trees with a size-limited 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 , , , , , | 9 Comments

The algebra of species: primitives

[This is the fifth in a series of posts about combinatorial species. Previous posts: And now, back to your regularly scheduled combinatorial species; Decomposing data structures; Combinatorial species definition, Species definition clarification and exercises.] Recall that a species is a … Continue reading

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Species definition clarification and exercises

[This is the fourth in a series of posts about combinatorial species. Previous posts: And now, back to your regularly scheduled combinatorial species; Decomposing data structures; Combinatorial species definition.] In my previous post I neglected to mention something quite crucial, … Continue reading

Posted in math, species | Tagged , , , | 2 Comments