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authorKarl Berry <karl@freefriends.org>2006-01-11 23:54:20 +0000
committerKarl Berry <karl@freefriends.org>2006-01-11 23:54:20 +0000
commit46a4138908c29f4b3feffadccf5f72da1fc9d171 (patch)
treec924763a4a23b0dad3516a810ed1dfad4094fcdf /Master/texmf-dist/source/latex/kuvio/doc-src/eg
parent75553bd842302454a6c00a4df2cc016411d7a4b4 (diff)
trunk/Master/texmf-dist/source/latex/kuvio
git-svn-id: svn://tug.org/texlive/trunk@343 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/source/latex/kuvio/doc-src/eg')
-rw-r--r--Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg01b.tex15
-rw-r--r--Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg02.tex23
-rw-r--r--Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg02A4.tex24
-rw-r--r--Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg03.tex30
-rw-r--r--Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg04.tex7
-rw-r--r--Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg05.tex22
-rw-r--r--Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg06a.tex15
-rw-r--r--Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg09.tex28
-rw-r--r--Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg12.tex13
-rw-r--r--Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg13.tex15
-rw-r--r--Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg15.tex10
-rw-r--r--Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg16.tex7
-rw-r--r--Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg17.tex14
-rw-r--r--Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg18.tex10
-rw-r--r--Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg19.tex20
-rw-r--r--Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg20.tex13
-rw-r--r--Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg20A4.tex13
-rw-r--r--Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg21.tex12
18 files changed, 291 insertions, 0 deletions
diff --git a/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg01b.tex b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg01b.tex
new file mode 100644
index 00000000000..72a787ce442
--- /dev/null
+++ b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg01b.tex
@@ -0,0 +1,15 @@
+$$
+\let~\tilde
+\cellwidth+=17mm \columndist+=12mm
+\gravitateleft
+\Dg
+ & & K & \rMono && E_1^\alpha& \rEpi^{\eta'}&& A' \\
+ & \ldTo& & && & & \ruBar \\
+~K& & \dBar\rMono\br& ~E_1^\alpha&& \dTo\rEpi^{~\eta'}\br&
+ A' \\
+\dBar& & & && & & & \dTo>\alpha \\
+ & & K & \rMono\dTo\br&& E_1\ax{2mm}& \rEpi\dTo\br&& A \\
+ & \ldTo& & & \ldTo& & & \ldBar \\
+~K& & \rMono & ~E_1 & \rEpi_{~\eta}& & A \\
+\endDg
+$$
diff --git a/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg02.tex b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg02.tex
new file mode 100644
index 00000000000..c0be43f6d9f
--- /dev/null
+++ b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg02.tex
@@ -0,0 +1,23 @@
+$$
+\dotted
+\grid=7mm
+\yscale=2
+\Diagram
+&&&&&&&&&xz&&&&xyz&&&&xy^2z&&&&xy^3z&\\
+\\
+z&&&&zy&&&&zy^2&&&&zy^3\\
+\dy{-.2}
+&&&&&&&&&x&&&&xy&&&&xy^2&&&&xy^3\\
+\\
+&&&&y&&&&y^2&&&&y^3\\
+\Modify
+\Line (0,0) (4,0) \dt{1pt}
+\Line (4,0) (8,0)
+\Line (8,0) (12,0)
+\Line (12,0) (22.5,0)
+\Line (0,0) (0,3) \dt{1pt}
+\Line (0,3) (0,5.2)
+\To (9,2) (12,0)
+\To (9,5) (12,3)
+\endDiagram
+$$
diff --git a/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg02A4.tex b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg02A4.tex
new file mode 100644
index 00000000000..919470e7b44
--- /dev/null
+++ b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg02A4.tex
@@ -0,0 +1,24 @@
+$$
+\dotted
+\grid=7mm
+\yscale=2
+\Diagrampad=0pt
+\Diagram
+&&&&&&&&&xz&&&&xyz&&&&xy^2z&&&&xy^3z&\\
+\\
+z&&&&zy&&&&zy^2&&&&zy^3\\
+\dy{-.2}
+&&&&&&&&&x&&&&xy&&&&xy^2&&&&xy^3\\
+\\
+&&&&y&&&&y^2&&&&y^3\\
+\Modify
+\Line (0,0) (4,0) \dt{1pt}
+\Line (4,0) (8,0)
+\Line (8,0) (12,0)
+\Line (12,0) (22.5,0)
+\Line (0,0) (0,3) \dt{1pt}
+\Line (0,3) (0,5.2)
+\To (9,2) (12,0)
+\To (9,5) (12,3)
+\endDiagram
+$$
diff --git a/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg03.tex b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg03.tex
new file mode 100644
index 00000000000..f068b6acdc4
--- /dev/null
+++ b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg03.tex
@@ -0,0 +1,30 @@
+$$
+\def\T{{\bf T}} \def\S{{\bf S}}
+\landscape \let\labelstyle\textstyle
+\cellpush=10pt \xscale=2.2
+\Diagram
+ & & H_n(X^+\cup\T A^+, X^+) &
+ \lTo ^{H_n(k_1)} & & H_n(\T A^+,A^+)
+ \aTo (-3,-2) _{H_n(p_1)}
+ \aTo (3,-4) ^{\partial_1} \\
+ & & \dTo >{H_n{q_1}} \\
+ & & H_n(\S A^+,P) &
+ & & * \dx{.7} \\
+ & \ruTo _{H_n(q_4)} \tx{15pt}
+ & \uTo >{H_n(t)} \\
+H_n(X^+\cup\T A^+,P) \aTo (2,4) ^{H_n(j_1)} \tx{15pt}
+ \aTo (2,-4) _{H_n(j_2)} \tx{15pt}
+ & & & & & & H_{n-1}(A) &
+ \rTo ^{H_{n-1}(i_A)} & H_{n-1}(A^+,P) \\
+ & \rdTo ^{H_n(q_2)} \tx{15pt}
+ & & & & \ruTo \\
+ & & H_n(X^+/A^+,P) &
+ \lTo ^{P_n(X,A)} & H_n(X,A)
+ \aTo (1,-2) >{H_n(i_X)} \\
+ & & \uTo >{H_n(q_3)} \\
+ & & H_n(X^+\cup\T A^+,\T A^+)&
+ \lTo _{H_n(k_2)} & & H_n(X^+,A^+)
+ \aTo (3,4) _{\partial_2}
+ \aTo (-3,2) _{H_n(p_X)} \\
+\endDiagram
+$$
diff --git a/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg04.tex b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg04.tex
new file mode 100644
index 00000000000..f9b8c2024ec
--- /dev/null
+++ b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg04.tex
@@ -0,0 +1,7 @@
+$$
+\Dg
+F\times K\times U & \rTo ^{\rm proj} & & K\times U \\
+\dTo & & & \dTo >{\rm proj} \\
+F\times_K (K\times U) & {} \approx F\times U & \rTo ^{\rm proj}& U \\
+\endDg
+$$
diff --git a/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg05.tex b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg05.tex
new file mode 100644
index 00000000000..a2b3d0518c5
--- /dev/null
+++ b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg05.tex
@@ -0,0 +1,22 @@
+$$
+\cellpush=4pt
+\let\labelstyle\textstyle
+\lpad=1in \bpad=1cm
+\Graph{4in,4}{3.5in,1in}
+\To (0,0) (3.3,0) \hd{p}
+\To (0,0) (0,3.5) \hd{q}
+\Line (2,0) (2,3.25) \Line (0,1) (3.2,1) \Dot (2,1)
+\Dot (0,0)
+%
+\Dot (2,0) \Dot (2.25,0) \Dot (2.5,0) \Dot (2.75,0) \Dot (3,0)
+%
+\Dot (0,1) \Dot (0,1.25) \Dot (0,1.5) \Dot (0,1.75)
+\Dot (0,2) \Dot (0,2.25) \Dot (0,2.5) \Dot (0,2.75) \Dot (0,3)
+%
+\Line (0,2.25) (2.5,0) ^{d^p} :{.35,5pt} \ro
+\Line (0,3) (3,0) ^{p + q = m + n} :{.35,5pt} \ro
+%
+\Math{q = n} (-.1,1) *1 \Math{E_{0,p-1}^2 = E_{0,p-1}^p} (-.1,2.25) *1
+\Math{p = m} (2,-.2) *{.55} \Math{E_{p,0}^2 = E_{p,0}^p} (2.75,-.2) *{.6}
+\endGraph
+$$
diff --git a/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg06a.tex b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg06a.tex
new file mode 100644
index 00000000000..5f06e3915bf
--- /dev/null
+++ b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg06a.tex
@@ -0,0 +1,15 @@
+$$
+\grid=.75cm
+\Diagram
+A' & & \rTo ^{f'} & & B' \\
+ & \rdTo <a \dh{2pt}& & & & \rdTo _b \\
+\dTo <{g'} & & A & & \dTo <{h'} :{.25}
+ \rTo ^f :{.25} \br
+ & & B \\
+ \\
+C' & & \rTo ^{k'} :{.75} \dTo <g :{.25} \br
+ & & D' & & \dTo >h \\
+ & \rdTo _c \dh{.5pt}&& & & \rdTo _d \\
+ & & C & & \rTo ^k & & D \\
+\endDiagram
+$$
diff --git a/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg09.tex b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg09.tex
new file mode 100644
index 00000000000..402af156440
--- /dev/null
+++ b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg09.tex
@@ -0,0 +1,28 @@
+$$
+\rotatedlabels \let\labelstyle\textstyle \scale=2
+\Diagram
+ & & F(3,2) \aLine (1,-4) >{F(3,1,1)} :{.4} \br \\
+ & & & \rdLine >{F(1,2,2)} \pt{right,.75} \\
+ & & & & F(1,4) \\
+F(2,3) \aDash (4,1) ^{F(1,1,3)} :{.4} \pp \\
+ & & & F(4,1) \aLine (1,2) >{F(1,3,1)} \\
+\Modify
+\Pt{top} (2,4) \Pt{b1} (0,1) \Pt{b2} (3,0)
+\Pt{LeftF} (1.65,2) \Pt{BackF} (2,2.5)
+\Pt{BottomF} (2.5,1) \Pt{RightF} (3.1,2.25)
+\Nul \pt{b1} \pt{b2} \pt{bottom,.8}
+\Nul \pt{BottomF} \pt{bottom} \pt{BottomL,2}
+\Dash \pt{BottomF} \pt{bottom} \tl\circ \dt{3pt}
+\Line \pt{bottom} \pt{BottomL} \hd{F(1,1,2,1)}
+\Line \pt{b1} \pt{b2} _{F(2,2,1)} \br
+\Nul \pt{b1} \pt{top} \pt{left,.25} \pt{back,.75}
+\Nul \pt{BackF} \pt{back} \pt{BackL,2}
+\Nul \pt{LeftF} \pt{left} \pt{LeftL,2}
+\Dash \pt{BackF} \pt{back} \tl\circ \dt{3pt}
+\Line \pt{back} \pt{BackL} \hd{F(1,1,1,2)}
+\Line \pt{b1} \pt{top} <{F(2,1,2)} \br
+\Line \pt{LeftF} \pt{LeftL} \tl\bullet \hd{F(2,1,1,1)} \jt \br
+\Nul \pt{RightF} \pt{right} \pt{RightL,3}
+\Line \pt{RightF} \pt{RightL} \tl\bullet \hd{F(1,2,1,1)} \jt \br
+\endDiagram
+$$
diff --git a/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg12.tex b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg12.tex
new file mode 100644
index 00000000000..383bdc4f632
--- /dev/null
+++ b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg12.tex
@@ -0,0 +1,13 @@
+$$
+\def\y#1#2{Y(#1,#2)} \def\RP{{\bb R}P}
+\gravitateright
+\Dg
+&&&\RP^1 = {}& \y11 & \rInto & \y21 & \rInto & \y31 & \rInto & \y41 & \rInto & \cdots \\
+&&& & & & \dTo & & \dTo & & \dTo & \\
+&&\RP^2 = {}&& & & \y12 & \rInto & \y22 & \rInto & \y32 & \rInto & \cdots \\
+&& && & & & & \dTo & & \dTo & \\
+&\RP^3 = {}&&& & & & & \y13 & \rInto & \y23 & \rInto & \cdots \\
+& &&& & & & & & & \dTo & \\
+\RP^4 = {}&&&& & & & & & & \y14 & \rInto & \cdots \\
+\endDg
+$$
diff --git a/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg13.tex b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg13.tex
new file mode 100644
index 00000000000..be4727420fe
--- /dev/null
+++ b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg13.tex
@@ -0,0 +1,15 @@
+$$
+\joined \let\labelstyle\textstyle
+\Graph{3cm,2}{3cm,4}
+\Line (0,0) (0,4) <{f(z,s)}
+\Line (0,4) (2,4) ^{H(z,t)}
+\Line (0,0) (2,0) _{*}
+\Line (2,0) (2,4)
+\Line (0,4) (2,2) _{\;\;H(z,0) = f(z,1)} \ro
+\endGraph
+\qquad\qquad
+H'(z,t,s) =
+\cases{f(z,2s/(2-t))& if $0\le 2s\le 2 - t$\cr
+ \cr
+ H(z,2s - 2 + t)& if $2 - t\le 2s\le 2$\cr}
+$$
diff --git a/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg15.tex b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg15.tex
new file mode 100644
index 00000000000..7c5c0f3fa31
--- /dev/null
+++ b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg15.tex
@@ -0,0 +1,10 @@
+$$
+\def\mod{\mathrel{\big/}}
+\Dg
+{\rm Spin}(3) & & & & SU(2) \\
+ & \rdTo & & \ldTo \\
+ & & SO(3) \\
+ & & \dTo \\
+& O(3)\mod O(1)^3 = {} & SO(3)\mod(O(1)^3\cap SO(3)) \\
+\endDg
+$$
diff --git a/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg16.tex b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg16.tex
new file mode 100644
index 00000000000..43a47a43d5a
--- /dev/null
+++ b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg16.tex
@@ -0,0 +1,7 @@
+$$
+\Dg
+u & \rTo ^{e_1} & v & & \rTo \up{3pt} ^f \rTo \up{-3pt} _g & d \\
+\uDashto >s & & \dTo >e & & & \uTo \\
+w & \rTo ^{ee_1s} & w & {} = {\mit\Pi}k_i & \rTo & k_i \\
+\endDg
+$$
diff --git a/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg17.tex b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg17.tex
new file mode 100644
index 00000000000..b2520a89fbf
--- /dev/null
+++ b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg17.tex
@@ -0,0 +1,14 @@
+$$
+\def\cod{{\rm cod}\,} \def\dom{{\rm dom}\,}
+\cellwidth+=2mm
+\Dg
+& F & _{\cod u} & \rEq & F & _{\cod u} & & & F_i \\
+& \uTo >{p_u} & & & \uTo & & & \ruTo <{p_i} \tx{-5pt} &
+ \uDashto >{\mu_i} \\
+{\mit\Pi}_{u:j\to k}F_k = {\mit\Pi}_u &
+ F & _{\cod u} & \lTo ^f \up{3pt} \lTo _g \up{-3pt}
+ & {\mit\Pi}_i & & F_i & \lDashto ^e & d \\
+& \dTo >{p_u} & & & \dTo >{p_{\dom u}} \\
+& F & _{\cod u} & \lTo ^{Fu} & F & _{\dom u} \\
+\endDg
+$$
diff --git a/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg18.tex b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg18.tex
new file mode 100644
index 00000000000..6d7791320ec
--- /dev/null
+++ b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg18.tex
@@ -0,0 +1,10 @@
+$$
+\cellwidth+=3mm
+\Dg
+Y & \rMono ^y & A & \rLine \jh & \stop \\
+\dEpi & & \dEpi & & \mx{-1cm} \\
+D & \rMono ^d & i_A(A) & & \dLine >{\eta_A} \jn \\
+\dMono & & \dMono \\
+X & \rMono _x & \overline{i_A(A)} & \lTo \jt & \stop \\
+\endDg
+$$
diff --git a/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg19.tex b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg19.tex
new file mode 100644
index 00000000000..b8e0400f203
--- /dev/null
+++ b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg19.tex
@@ -0,0 +1,20 @@
+$$
+\cellpush+=5pt
+\cellwidth+=2mm
+\Dg
+&&_{N+t'}X_p & \rTo ^{g_{p+q}} & _N X_{p+q} \\
+&& \dFillcell{\;\cdots\;\rightarrowfill} &
+ & \dFillcell{\;\cdots\;\rightarrowfill} \\
+ \\
+&& _{N+t'}X_1 & \rTo ^{g_{q+1}} & _N X_{q+1} \\
+&& \dTo & & \dTo \\
+S^{N+t+t'}X \aTo (2,5) ^{f_p} \tx{.7} \hx{5pt} & \rTo ^f &
+ S^{N+t'}X & \rTo ^{g_q} & _N X_q \\
+ \\
+&& & & \dFillcell{\rightarrowfill\;\cdots\;\rightarrowfill} \\
+ \\
+&& & & _N X_1 \\
+&& & & \dTo \\
+&& & & S^N X \bTo (-2,6) <g \hx{.2} \\
+\endDg
+$$
diff --git a/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg20.tex b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg20.tex
new file mode 100644
index 00000000000..5f5b1d74a96
--- /dev/null
+++ b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg20.tex
@@ -0,0 +1,13 @@
+$$
+\let\^\widehat \let\~\widetilde
+\flexible \columndist=1cm
+\xgrid+=2mm \ygrid+=-2mm
+\Diagram
+ & & & &H^0 \bTo(-1,-4) \hx{-2pt}
+ &\cdots &H^{n-1} &H^n &H^{n+1} &H^{n+2} &\cdots \\
+\mx{5mm}& & & &\dTo & &\dTo &\dEpi&\dBar &\dBar &\mx{-2mm}\\
+\cdots &\^H^{-3} &\^H^{-2} &\^H^{-1}&\^H^0 &\cdots &\^H^{n-1}&\^H^n&\^H^{n+1}&\^H^{n+2}&\cdots\\
+ &\dBar &\dBar &\dInto &\dTo & &\dTo \dx{-2mm} \\
+\cdots &\~H_{n+2}&\~H_{n+1}&\~H_n &\~H_{n-1}&\cdots&\~H_0 \aTo(1,4) \hx{-2pt} \\
+\endDiagram
+$$
diff --git a/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg20A4.tex b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg20A4.tex
new file mode 100644
index 00000000000..6be4f5a5d64
--- /dev/null
+++ b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg20A4.tex
@@ -0,0 +1,13 @@
+$$
+\let\^\widehat \let\~\widetilde
+\flexible \columndist=1cm
+\xgrid+=2mm \ygrid+=-2mm
+\Diagram
+ & & & &H^0 \bTo(-1,-4) \hx{-2pt}
+ &\cdots&H^{n-1} &H^n &H^{n+1}&H^{n+2} &\cdots \\
+\mx{5mm}& & & &\dTo & &\dTo &\dEpi&\dBar &\dBar &\mx{-2mm}\\
+\cdots&\^H^{-3} &\^H^{-2} &\^H^{-1}&\^H^0 &\cdots&\^H^{n-1}&\^H^n&\^H^{n+1}&\^H^{n+2}&\cdots\\
+ &\dBar &\dBar &\dInto &\dTo & &\dTo \dx{-2mm} \\
+\cdots&\~H_{n+2}&\~H_{n+1}&\~H_n&\~H_{n-1}&\cdots&\~H_0 \aTo(1,4) \hx{-2pt} \\
+\endDiagram
+$$
diff --git a/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg21.tex b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg21.tex
new file mode 100644
index 00000000000..a93205708bd
--- /dev/null
+++ b/Master/texmf-dist/source/latex/kuvio/doc-src/eg/eg21.tex
@@ -0,0 +1,12 @@
+$$
+\def\M{{\cal M}\dot} \def\inv{^{-1}} \def\orlz#1{\langle#1\rangle}
+\let\labelstyle\textstyle
+\Dg
+[q(g,b),t] \aNul (1,-1) \aMapsto (2,-4) &&& \rMapsto &&&
+ q(g,\phi(b,t)) \aNul (-1,-1) \aMapsto (-2,-4) \mx{12pt} \\
+ & \M R_s & & \rTo & & \beta\inv(W_s) \\
+ & & \rdTo & & \ldTo >{R_s} \\
+ & & & \beta\inv\orlz{s} \\
+ & & q(g,r_s(b)) & {} = {} & q(g,r_s(\phi(b,t))) \\
+\endDg
+$$