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  • Jan 31 2019 03:07
    SethTisue commented #219
  • Jan 30 2019 21:49
    keithschulze starred typelevel/algebra
  • Jan 30 2019 20:19

    larsrh on gh-pages

    updated site (compare)

  • Jan 30 2019 20:11

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    updated site (compare)

  • Jan 30 2019 19:56

    larsrh on revert-216-docs

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  • Jan 30 2019 19:56

    larsrh on master

    Revert "fix homepage (#216)" T… Merge pull request #220 from ty… (compare)

  • Jan 30 2019 19:56
    larsrh closed #220
  • Jan 30 2019 19:55
    larsrh commented #219
  • Jan 30 2019 19:55
    larsrh closed #219
  • Jan 30 2019 19:55

    larsrh on v1.0.1

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  • Jan 30 2019 19:55

    larsrh on master

    Setting version to 1.0.1 Setting version to 1.0.2-SNAPSH… (compare)

  • Jan 30 2019 18:05

    larsrh on gh-pages

    updated site (compare)

  • Jan 30 2019 17:54

    johnynek on master

    build for 2.13.0-M5 (#223) * b… (compare)

  • Jan 30 2019 17:54
    johnynek closed #223
  • Jan 30 2019 16:41
    sungjk starred typelevel/algebra
  • Jan 30 2019 14:28
    erikerlandson commented #223
  • Jan 30 2019 13:58
    tusharbihani starred typelevel/algebra
  • Jan 30 2019 13:39
    larsrh commented #223
  • Jan 30 2019 13:37
    erikerlandson commented #223
  • Jan 30 2019 13:30
    larsrh commented #223
jeremyrsmith
@jeremyrsmith
inspired by @tpolecat’s diagrams of cats’ typeclass hierarchy (though not nearly as nice)
(it is pretty small on the gist preview, but if you right-click and open image in new tab it looks alright)
it’s an interesting question: what does it mean to be an additive or multiplicative group in the absence of the other (within a ring)
jeremyrsmith
@jeremyrsmith
If a non-armchair mathematician has an answer I’d be fascinated to hear. I’m thinking something about multiplicative groups being combinatorial in nature, but it doesn’t seem like you can know that without “cheating” and looking at the structure of the group. Also I think there’s something there about relating a ring to a monad via multiply (eta) and add (mu). But as an armchair mathematician, I’ll leave it to the experts.
Luka Jacobowitz
@LukaJCB
Awesome stuff @jeremyrsmith
Srepfler Srdan
@schrepfler
what do you mean @jeremyrsmith by "to be an additive or multiplicative group in the absence of the other (within a ring)”?
jeremyrsmith
@jeremyrsmith
just that they’re structurally indistinguishable from one another, unless they’re both part of a ring structure
if you have a ring structure, then you have two group structures and you know which is additive and which is multiplicative by the nature of multiplication distributing over addition (at least)
if all you have is a group structure, there is no structural way to say whether it’s additive or multiplicative, without “peeking"
(as far as I can determine)
Srepfler Srdan
@schrepfler
I think in abstract algebra the terms additiona and multiplication are mostly inherited from historical baggage of dealing with numbers
a Zero and One are both a Neutral element of the group
and Negate and Invert are the Reciprocal of the value relative to the Neutral
the fact that you have two operations which follow these rules
that defines the Ring
No grups, no ring
both addition and multiplications are a function from two operands to one
Srepfler Srdan
@schrepfler
So I imagine what the guys want to say is here's a framework on how to reason if computations which are chained have a result in the end since it will tell you if you have holes in your domain and arrival set
and then the category theory guys kind of expanded that
Denis Rosset
@denisrosset
There are a few things between "commutative ring" and "field", such as "unique factorization domain" and "euclidean ring".
Wikipedia is pretty complete on that
Ghost
@ghost~529c6cf4ed5ab0b3bf04da61
Can I get a :+1: on this? #217
I'm trying to aid in moving everyone to M5
Ghost
@ghost~529c6cf4ed5ab0b3bf04da61
#223 will update everything necessary for M5
Denis Rosset
@denisrosset
Thanks!