Cammy/Bikeshed
Cammy/Bikeshed - Esolang
This page is an appendix for research done for Cammy which is too long and boring to be included on the main page.

Nomenclature
Most categorical objects are each a presentation of some wikipedia:universal property, but the current practice of mathematics does not have unambiguous symbols for most of them. Worse, most arrows do not have standard names, and sometimes not even standard titles.
The following table's rows are categorical arrows, and the columns are category theorists who have named them; each cell is a name. Our columns are:

Curien 1986
Hagino 1987
Von Thun 2001
Kerby 2002
Baez & Stay 2009
Elliott 2017
Patterson 2017
In addition, we have three extra columns. Two are for the communities of Wikipedia and nLab respectively, and one is for Cammy.

Kerby's Category
Kerby gives a broad argument that their `i` combinator, which unquotes a
single quotation and executes its stack effect, is a homomorphism. Indeed, we
will imagine an entire category which routes quotations opaquely without
executing them; to execute any expression in Kerby's category, simply suffix
it with `i`. However, Kerby also gives a persuasive argument that lambda
calculus is best understood with the identity arrow being the expression
`A\A`, which corresponds precisely to `i`. We thus will use `i` for identity
and reason from there.

Delta
One might expect that the usage of the Greek capital wikipedia:delta (letter) is definitely the Unicode codepoint U+0394 GREEK CAPITAL LETTER DELTA. However, Baez & Stay and Patterson use U+2206 INCREMENT, and Elliott uses U+25b3 WHITE UP-POINTING TRIANGLE. This is almost certainly a typesetting issue. The table uses U+0394 (Δ) exclusively, for screen readers.



WP
nLab
Cammy
Curien
Hagino
Von Thun
Kerby
Baez & Stay
Elliott
Patterson


wikipedia:morphism#Identity
[1]
id
id
-
id
i
id
id
1


-
[2]
comp
◦
-
-
b
◦
◦
-


wikipedia:initial and terminal objects
[3]
ignore
1
!
drop
zap
!
it
I


wikipedia:product (category theory)
[4]
fst
Fst
pi1
pop
k
p
exl
-


…
…
snd
Snd
pi2
popd
z
p'
exr
-


…
…
pair
<,>
pair
-
c
-
Δ
-


…
…
pair/tensor
-
prod
-
-
⊗
-
⊗


wikipedia:diagonal morphism
[5]
pair/dup
-
-
dup
dup
Δ
-
Δ


wikipedia:coproduct
[6]
left
-
in1
-
-
-
inl
-


…
…
right
-
in2
-
-
-
inr
-


…
…
case
-
case
-
-
-
jam
-


wikipedia:monoidal category
[7]
assl
-
-
-
-
assoc
-
-


…
…
assr
-
-
-
-
-
-
-


wikipedia:free monoid
[8]
nil
-
nil
[]
-
-
-
-


…
…
cons
-
cons
cons
-
-
-
-


…
…
fold
-
prl
fold
-
-
-
-


wikipedia:symmetric monoidal category
[9]
swap
-
-
swap
swap
braid
-
σ


wikipedia:Cartesian closed category
[10]
curry
Λ
curry
-
-
~
curry
-


…
…
uncurry
-
-
-
-
-
uncurry
-


…
…
app
App
eval
b
-
eval
apply
-


wikipedia:natural numbers object
[11]
zero
-
zero
0
z0
-
-
-


…
…
succ
-
succ
succ
-
-
-
-


…
…
pr
-
pr
primrec
-
-
-
-






