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Subject: Re: Functionally complete/universal basis for graph homomorphisms?
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Patrik Eklund wrote:

I will under the CATLIST and at this point not reply more in detail, but
>
let me just now say that your "categories are not algebraic in sets, at
> least they are algebraic in graphs, which in turn are algebraic in sets"
> is within the realm of "algebraic categories".
>

That depends on your definition of "algebraic categories".  There are a
number
of inequivalent definitions in common use:

https://ncatlab.org/nlab/show/algebraic+category

What definition are you using above?

Best,
jb

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<div dir=3D"ltr">Patrik Eklund wrote:<br><br><div><div class=3D"gmail_extra=
"><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;borde=
r-left:1px solid rgb(204,204,204);padding-left:1ex">I will under the CATLIS=
T and at this point not reply more in detail, but<br></blockquote><div clas=
s=3D"gmail_quote"><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px=
  0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
let me just now say that your &quot;categories are not algebraic in sets, a=
t<span class=3D"gmail-"><br>
least they are algebraic in graphs, which in turn are algebraic in sets&quo=
t;<br></span>
is within the realm of &quot;algebraic categories&quot;.<br></blockquote><d=
iv><br></div><div>That depends on your definition of &quot;algebraic catego=
ries&quot;.=C2=A0 There are a number</div><div>of inequivalent definitions =
in common use:</div></div><div class=3D"gmail_quote"><br></div><div class=
=3D"gmail_quote"><a href=3D"https://ncatlab.org/nlab/show/algebraic+categor=
y">https://ncatlab.org/nlab/show/algebraic+category</a></div><div class=3D"=
gmail_quote"><br></div><div class=3D"gmail_quote">What definition are you u=
sing above?</div><div class=3D"gmail_quote"><br></div><div class=3D"gmail_q=
uote">Best,</div><div class=3D"gmail_quote">jb<br></div></div></div></div>

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