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# Category Archives: math

## Pan-Galactic Division in Haskell

Summary: given an injective function , it is possible to constructively “divide by ” to obtain an injection , as shown recently by Peter Doyle and Cecil Qiu and expounded by Richard Schwartz. Their algorithm is nontrivial to come up … Continue reading

## Polynomial Functors Constrained by Regular Expressions

I’ve now finished revising the paper that Dan Piponi and I had accepted to MPC 2015; you can find a PDF here: Polynomial Functors Constrained by Regular Expressions Here’s the 2-minute version: certain operations or restrictions on functors can be … Continue reading

Posted in math, writing
Tagged differentiation, dissection, functor, matrices, polynomial, regular expression, semirings
5 Comments

## 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
5 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