Sample HTML file: produced with lwarp, with mathematical formulae displayed with MathJax, and xymatrix commutative diagrams displayed with XyJax-v3

2 Examples: xymatrix diagrams displayed with Xy-Jaxv3 using Lwarp

This is an example of a HTML file with:

• • Mathematical formulae displayed with MathJax:

  \(\seteqnumber{0}{}{0}\)

  \begin{equation} \label {test} x^2+y^2=1, \end{equation}

  \[\big ( x \ra { \gamma } y\big ) \in \pi _1(X,X_0), \]

  \[ \dots \to \pi _i(E_b,x) \ra {\iota } \pi _i(E,x) \ra {\d } \pi _i(B,b) \ra {\delta } \pi _{i-1}(E_b,x) \to \dots \ra {\iota } \pi _1(E,x) \ra {\partial } \pi _1(B,b) \ra {\delta _x} \pi _0(E_b) \ra {\iota } \pi _0(E)=\{0\}. \]

• • To see how lecture notes look like with Lwarp, see subsections 6.1 and 6.2.

• • This configuration is compatible with AMS-CD commutative diagrams, e.g. this diagram from the amscd package manual:

  \[ \begin {CD} A @>a>b> B\\ @VlVrV @AlArA\\ C @<a<b< D \end {CD} \]

• • Commutative diagrams drawn with Xy-pic displayed by using XyJax-v3.
  For a good introduction to typeseting diagrams with Xy-pic see e.g.

  • – https://www.math.purdue.edu/~adebray/lecture_notes/using_xy.pdf (Arun Debray Using XY to typeset automata. July 5, 2016.)

  • – https://web.math.ku.dk/~holm/download/xyrefer.pdf (Kristoffer H. Rose & Ross Moore: XY-pic Reference Manual, Version 3.7 1999/02/16.)

  • – See also the more recent user guide (Kristoffer H. Rose, Version 3.8.9, October 6, 2013) in the official page of xymatrix – Commutative diagrams using XY-pic

  E.g.

  \[\xymatrix @R=60pt@C=60pt{&S_3 \ar @{^{(}->}[r]^f \ar [dr]_{g}^{\cong } &S_4 \ar @{->>}[d]^\pi \\ &&S_4/V, } \]

  \[ \xymatrix { && \Q \\ & \Q (\w ) \ar @{<-}[ur] \\ & & \Q (\g )\ar @{<-}[uu] & \Q (\b )\ar @{<-}[uul] & \Q (\a ),\ar @{<-}[uull]\\ &&\Q (\a ,\b ,\g )\ar @{<-}[uul]\ar @{<-}[u] \ar @{<-}[ur] \ar @{<-}[urr] } \]

  \[\xymatrix @R=1pt{\\\\\\(123).}\xymatrix @R=39pt{ & \red {\bullet }\ar @{-}[dr] \ar @{-}[rr] && \blue {\star }\ar @{-}[dl] \\ && \green {\square } }\qquad \xymatrix @R=1pt{\\\\\\\\ =} \xymatrix @R=39pt{ & \blue {\star }\ar @{-}[dr] \ar @{-}[rr] && \green {\square }\ar @{-}[dl] \\ && \red {\bullet } } \xymatrix @R=1pt{\\\\\\\\ ,}\]

  \[\xymatrix @R=30pt@C=60pt {&A\ar [d]_{{\iota _0}^A} \ar [r]^f & X\ar [d]_{{\iota _0}^X} \ar [r]^g & B,\\ & A \times I \ar @/_4pc/[rru]_<<<<<<<<<<<{H} \ar [r]^{f \times \id _I} & X\times I \ar @{-->}[ur]^{H'} } \]

  \[ \xymatrix { & \displaystyle \bigoplus _{y \in H_0} \mathbf {H}_1(x,y)\otimes \mathbf {H}_1'(y,z)\ar [dd]_{\displaystyle \bigoplus _{y \in H_0} \eta _{(x,y)} \otimes \eta '_{(y,z)}} \ar [rr]^{\mathrm {proj}} && \displaystyle \int ^{y \in H_0} \mathbf {H}_1(x,y)\otimes \mathbf {H}_1'(y,z)\ar @{-->}[dd]^{ \displaystyle \int ^{y \in Y} \eta _{(x,y)} \otimes \eta '_{(y,z)} }\\ \\ & \displaystyle \bigoplus _{y \in H_0} \mathbf {H}_2(x,y)\otimes \mathbf {H}_2'(y,z) \ar [rr]_{\mathrm {proj}} && \displaystyle \int ^{y \in H_0} \mathbf {H}_2(x,y)\otimes \mathbf {H}_2'(y,z)\,\, , } \]

  \[\xymatrix { &\displaystyle \int ^{y \in {Y}} \Hpb _{(X,Y)}^{M_1}(-,y) \otimes \Hpb _{(Y,Z)}^{M_2}(y,-)\ar @{=>}[dd]|{\tHpb {\mathbf {W}_1}{X}{Y} \bullet \tHpb {\mathbf {W}_2}{Y}{Z}} \ar @{=>}[rrr]^>>>>>>>>>>>>>>>>>{\eta _{(X,Y,Z)}^{M_1,M_2}}&&& \Hpb _{(X,Z)}^{M_1\times _Y M_2} \ar @{=>}[dd]|{\tHpb {\mathbf {W}_1\#_0 \mathbf {W}_2}{X}{Z}} \\\\ &\displaystyle \int ^{y \in {Y}} \Hpb _{(X,Y)}^{N_1}(-, y) \otimes \Hpb _{(Y,Z)}^{N_2}(y,-)\ar @{=>}[rrr]^>>>>>>>>>>>>>>>>>{\eta _{(X,Y,Z)}^{N_1,N_2}}&&& \Hpb _{(X,Z)}^{N_1\times _Y N_2}\,. } \]

  \[\xymatrix { &\Cc \rtwocell ^F_{F'}{\eta } &\Dc } \]

  \[\hskip -0.5cm\xymatrix @C=25pt@R=30pt{& T\times T\ar [drr]_{\sqcup } \ar [rr]^{ \tau } &\drtwocell \omit {\,\,\, \mathbf {R}}& T \times T \ar [d]^{\sqcup } \\ &&& T.} \]

  \[\xymatrix @C=45pt{&\Cc \sqcup \Cc ' \rtwocell \omit {\quad \,\, \langle \eta ,\eta '\rangle } \ar @/^1.5pc/[r]^{T_b\circ \langle f, f' \rangle } \ar @/_1.5pc/[r]_{\langle T,T'\rangle } & \Grp . }\]

  \[ \xymatrix @C=60pt{\Cc \ruppertwocell ^F{\eta } \rlowertwocell _{F''}{\eta '} \ar [r]|{F''} & \Dc & = &\Cc \ar @/^1.5pc/[r]^{F}\ar @/_1.5pc/[r]_{F''}\rtwocell \omit {\quad \,\,\,\,\eta \#_1\eta '} & \Dc &} \]

  \[ \hskip -2cm\xymatrix @C=60pt{ &\big ( \mathbf {Cob}^{(n,n+1,n+2)}\big )^3 \ar [d]_{\id \times \sqcup }\ar [dr]^{\sqcup \times \id } \drrtwocell \omit {\qquad \boldsymbol {\chi }'\times \mathcal {F}_{\mathbf {B}}} \ddtwocell \omit {<-13> \alpha } \ar [rr]^{\mathcal {F}_{\mathbf {B}} \times \mathcal {F}_{\mathbf {B}} \times \mathcal {F}_{\mathbf {B}}} && \big (\mathbf {Prof} \big )^3\ar [d]^{\otimes \times \id }\\ &\big ( \mathbf {Cob}^{(n,n+1,n+2)})^2 \ar [d]_{\sqcup } & \big ( \mathbf {Cob}^{(n,n+1,n+2)})^2 \ar [dl]^{\sqcup } \dtwocell \omit { \boldsymbol {\chi }'} \ar [r]^{\mathcal {F}_{\mathbf {B}} \times \mathcal {F}_{\mathbf {B}}} & \big (\mathbf {Prof} \big )^2 \ar [dl]^{\otimes } \\ & \big (\mathbf {Cob}^{(n,n+1,n+2)}\big ) \ar [r]_{\mathcal {F}_{\mathbf {B}}}& \mathbf {Prof}\\ & \ar @3[r]_{\boldsymbol {\omega }'} & \\ &\big ( \mathbf {Cob}^{(n,n+1,n+2)}\big )^3 \ar [d]_{\id \times \sqcup } \drrtwocell \omit {\quad \qquad \mathcal {F}_{\mathbf {B}}\times \boldsymbol {\chi }' }\ar [rr]^{\mathcal {F}_{\mathbf {B}} \times \mathcal {F}_{\mathbf {B}} \times \mathcal {F}_{\mathbf {B}}} && \big (\mathbf {Prof} \big )^3\ddltwocell \omit {\alpha } \ar [d]^{\otimes \times \id }\ar [dl]^{\id \times \otimes }\\ &\big ( \mathbf {Cob}^{(n,n+1,n+2)})^2 \ar [d]_{\sqcup } \drtwocell \omit {\,\,\boldsymbol {\chi }' } \ar [r]^{\mathcal {F}_{\mathbf {B}} \times \mathcal {F}_{\mathbf {B}}} & \big ( \mathbf {Prof})^2 \ar [d]^{\otimes } & \big (\mathbf {Prof} \big )^2\ar [dl]^{\otimes }\\ & \big (\mathbf {Cob}^{(n,n+1,n+2)}\big ) \ar [r]_{\mathcal {F}_{\mathbf {B}}}& \mathbf {Prof}. } \]