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Phil Freeman
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@paf31

Phil Freeman

@paf31
Los Angeles
blog.functorial.com
Joined February 2011
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  • @paf31
    Phil Freeman
    @paf31
    Sep 2
    People like to describe comonads as being about "what you need from your environment" or something similar, which I have never liked. It's not a constructive explanation of e.g. why effects like State, Reader, Writer can be modeled using comonads but general IO can't.
    3
  • @paf31
    Phil Freeman
    @paf31
    Jul 23
    Game of Life on an infinite grid, implemented as the Day convolution of two zipper comonads.
    Image
    GOL using Day of two zipper comonads
    From gist.github.com
  • @paf31
    Phil Freeman
    @paf31
    Jul 19
    Very excited to put the old comonads work and "as spaces" intuition on a solid footing finally
    @CategoryPapers
    Category Theory Papers
    @CategoryPapers
    Jul 17
    Comonads as spaces Aaron David Fairbanks, Kevin Carlson, David I. Spivak arxiv.org/abs/2607.15091 [𝚖𝚊𝚝𝚑.𝙲𝚃]
    Comonads on Set generalize both categories and topological spaces. Expanding upon Garner's work on ionads, we develop aspects of the theory of topological spaces for arbitrary comonads on arbitrary categories. Our approach is centered around density comonads, which provide an abstraction of subbases. We study subbases as well as bases in terms of density comonads, and we study continuous maps of comonads in terms of functors between coalgebra categories, with definitions that recover the usual notions for topological spaces. Whereas Ahman and Uustalu characterized categories as precisely the polynomial comonads on Set, we characterize topological spaces as precisely the density comonads of diagrams of subsets of a set, which are familiar as topological subbases. We show that every comonad on Set has an underlying topological space, and that this construction is a reflection with respect to continuous maps; similarly, every comonad on Set has an underlying small category, and this const
    2
  • @paf31
    Phil Freeman
    @paf31
    May 27
    Made a little playground for iterated function systems
    Image
    00:00
    1
  • @paf31
    Phil Freeman
    @paf31
    Nov 24, 2025
    Just in case anyone is curious, yes, my personal website works on Netscape Navigator v2.0.2
    Image
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