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\begin{document}

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% https://mail.google.com/mail/ca/u/0/#inbox/FMfcgxwBVWJTPqxSMKgQQxBTSDdqCLjz

I have read your article in the latest Tugboat with interest and I have
some questions and comments.  The first diagram I would do using
 $$\bfig
 \square/<-|`>`>`|->/<400,400>[LA`A`B`RB;```]
\efig$$
 rather than 4 morphisms, but that's my preference.  (Incidentally, the
opening and closing come from NRoff, but I would likely do it with
braces today.)  An alternative way to make that square would be
 $$\bfig
 \node 1a(0,400)[LA]
 \node 1b(400,400)[A]
 \node 2a(0,0)[B]
 \node 2b(400,0)[RB]
 \arrow/|->/[1b`1a;] %%% alternately \arrow/<-|/[1a`1b;]
 \arrow[1a`2a;]
 \arrow[1b`2b;]
 \arrow/|->/[2a`2b;]
 \efig$$
   which is nearly self documenting.

In your second diagram, I fail to see where in your specification the
dashed arrow in the middle is specified, nor where sizes are.  Here
is how I would do that:
 $$\bfig
 \node 1(0,500)[A]
 \node 2a(-300,0)[FA]
 \node 2b(0,0)[\phantom A]
 \node 2c(300,0)[GA]
 \arrow/|->/[1`2a;]
 \arrow/-->/[1`2b;]
 \arrow/|->/[1`2c;]
 \arrow|b|[2a`2c;TA]
 \efig$$
 But I wonder how you would specify additional diagonal arrows.  For
example, how would you do
 $$\bfig
 \node 1(0,500)[A]
 \node 2x(-800,0)[HA]
 \node 2a(-300,0)[FA]
 \node 2b(0,0)[\phantom A]
 \node 2c(300,0)[GA]
 \node 2y(800,0)[KA]
 \arrow/|->/[1`2a;]
 \arrow/-->/[1`2b;]
 \arrow/|->/[1`2c;]
 \arrow|b|[2a`2c;TA]
 \arrow[1`2x;]
 \arrow[1`2y;]
 \arrow[2x`2a;]
 \arrow[2c`2y;]
 \efig$$

And what would you do with the following, taken from a recent paper of
mine?
 $$\bfig
 \node 1a(-500,500)[C]
 \node 1b(0,500)[X]
 \node 1c(500,500)[C]
 \node 2(0,0)[Y]
 \arrow[1a`1b;f]
 \arrow[1b`1c;g]
 \arrow/@{->}@<-3pt>/[1b`2;k]
 \arrow/@{->}@<-3pt>/[2`1b;\ell ]
 \arrow|l|[1a`2;kf]
 \arrow|r|[2`1c;g\ell ]
 \efig$$
 or (horrors) taken from a paper I copy-edited for TAC:
 $$\bfig
 \node 1(1000,800)[Y]
 \node 21(0,0)[X]
 \node 22(2000,0)[Z]
 \node aa(300,400)[]
 \node ab(450,400)[]
 \node ba(1550,400)[]
 \node bb(1700,400)[]
 \arrow|a|/{@{>}@/^20pt/}/[21`1;f]
 \arrow|b|[21`1;g]
 \arrow[aa`ab;\beta]
 \arrow[bb`ba;\delta]
 \arrow|b|[1`22;i]
 \arrow|a|/{@{>}@/^20pt/}/[1`22;h]
 \arrow/{@{>}@/^15pt/@<5pt>^(.4)k}/[21`22;]
 \arrow/{@{>}@/^15pt/@<5pt>^(.4)k}/[21`22;]
 \arrow/{@{>}@<5pt>|(.4)j|(.5)\hole}/[21`22;]
 \arrow/{@{>}@<-10pt>|(.4){hf}|-\hole}/[21`22;]
 \arrow/{@{>}@/_15pt/@<-10pt>_(0.4){ig}}/[21`22;]
 \node c(1000,150)[]
 \node f(1000,-200)[]
 \arrow|l|[f`c;t]
 \node d(1100,25)[]
 \node e(1100,-75)[]
 \arrow|r|[e`d;s]
 \efig$$



\end{document}

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