Skip to content

Commit

Permalink
polish: "surjective head" style
Browse files Browse the repository at this point in the history 
Closes #215
  • Loading branch information
@vEnhance
vEnhance committed Nov 18, 2023
1 parent a980977 commit 32cde85
Show file tree
Hide file tree
Showing 9 changed files with 53 additions and 49 deletions.
2 changes: 1 addition & 1 deletion tex/H113/structure.tex
View file
Original file line number Diff line number Diff line change
Expand Up @@ -225,7 +225,7 @@ \section{Reduction to maps of free $R$-modules}
\begin{center}
\begin{tikzcd}
& K \ar[rd, hook] \\
R^{\oplus f} \ar[ru, two heads] \ar[rr, "T"'] && R^{\oplus d} \ar[r, two heads] & M
R^{\oplus f} \ar[ru, surjective head] \ar[rr, "T"'] && R^{\oplus d} \ar[r, surjective head] & M
\end{tikzcd}
\end{center}
Observe that $M$ is the \emph{cokernel} of the linear map $T$,
Expand Down
6 changes: 3 additions & 3 deletions tex/alg-NT/artin.tex
View file
Original file line number Diff line number Diff line change
Expand Up @@ -374,8 +374,8 @@ \section{Artin reciprocity}
the above theorem tells us we get a sequence of maps
\begin{center}
\begin{tikzcd}
I_K(\kf) \ar[r, two heads] & C_K(\kf) \ar[rd, two heads]
\ar[rr, "\left( \frac{L/K}{\bullet} \right)", two heads]
I_K(\kf) \ar[r, surjective head] & C_K(\kf) \ar[rd, surjective head]
\ar[rr, "\left( \frac{L/K}{\bullet} \right)", surjective head]
&& \Gal(L/K) \\
&& I_K(\kf) / H(L/K, \kf) \ar[ru, "\cong", swap] &
\end{tikzcd}
Expand Down Expand Up @@ -472,7 +472,7 @@ \section{Artin reciprocity}
I_K(\km)
\ar[r, "\left( \frac{M/K}\bullet \right)"]
\ar[rd, "\left( \frac{L/K}\bullet \right)", swap]
& \Gal(M/K) \ar[d, two heads] \\
& \Gal(M/K) \ar[d, surjective head] \\
& \Gal(L/K)
\end{tikzcd}
\end{center}
Expand Down
6 changes: 3 additions & 3 deletions tex/alg-geom/bezout.tex
View file
Original file line number Diff line number Diff line change
Expand Up @@ -166,7 +166,7 @@ \section{Hilbert functions of finitely many points}
\begin{tikzcd}
0 \ar[r]
& \left[ S / (I \cap J) \right]^d \ar[r, hook]
& \left[ S / I \right]^d \oplus \left[ S / J \right]^d \ar[r, two heads]
& \left[ S / I \right]^d \oplus \left[ S / J \right]^d \ar[r, surjective head]
& \left[ S / (I+J) \right]^d \ar[r] & 0 \\
& f \ar[r, mapsto] & (f,f) \\
&& (f,g) \ar[r, mapsto] & f-g
Expand Down Expand Up @@ -302,7 +302,7 @@ \section{Hilbert polynomials}
\begin{tikzcd}
0 \ar[r]
& \left[ S/I \right]^{d-1} \ar[r, hook]
& \left[ S / I \right]^d \ar[r, two heads]
& \left[ S / I \right]^d \ar[r, surjective head]
& \left[ S / (I+(f)) \right]^d \ar[r] & 0 \\
& f \ar[r, mapsto] & f \cdot x_0 \\
&& f \ar[r, mapsto] & f.
Expand Down Expand Up @@ -365,7 +365,7 @@ \section{B\'ezout's theorem}
\begin{tikzcd}
0 \ar[r]
& \left[ S/I \right]^{d-k} \ar[r, hook]
& \left[ S / I \right]^d \ar[r, two heads]
& \left[ S / I \right]^d \ar[r, surjective head]
& \left[ S / (I+(f)) \right]^d \ar[r] & 0.
\end{tikzcd}
\end{center}
Expand Down
20 changes: 10 additions & 10 deletions tex/cats/abelian.tex
View file
Original file line number Diff line number Diff line change
Expand Up @@ -49,7 +49,7 @@ \section{Zero objects, kernels, cokernels, and images}
The \vocab{cokernel} of $f$ is a map $\coker f \colon B \surjto \Coker f$ such that
\begin{center}
\begin{tikzcd}
A \ar[r, "f"] \ar[rd, "0"', dashed] & B \ar[d, "\coker f", two heads] \\
A \ar[r, "f"] \ar[rd, "0"', dashed] & B \ar[d, "\coker f", surjective head] \\
& \Coker f
\end{tikzcd}
\end{center}
Expand Down Expand Up @@ -78,7 +78,7 @@ \section{Zero objects, kernels, cokernels, and images}
\begin{center}
\begin{tikzcd}
A \ar[rd, "\exists!"'] \ar[rr, "f"] \ar[rrrd, "0"', near start, dashed]
&& B \ar[rd, two heads, "\coker f"] \\
&& B \ar[rd, surjective head, "\coker f"] \\
& \Img f \ar[ur, hook] \ar[rr, "0", dashed] && \Coker f
\end{tikzcd}
\end{center}
Expand Down Expand Up @@ -118,8 +118,8 @@ \section{Additive and abelian categories}
\Img(f) \ar[rd, hook]
&&
\Coker(f) \\
& A \ar[ru, "\img(f)", two heads] \ar[rr, "f"', dashed]
&& B \ar[ru, "\coker(f)"', two heads]
& A \ar[ru, "\img(f)", surjective head] \ar[rr, "f"', dashed]
&& B \ar[ru, "\coker(f)"', surjective head]
\end{tikzcd}
\end{center}
\end{definition}
Expand Down Expand Up @@ -215,7 +215,7 @@ \section{Exact sequences}
Adding in all the relevant objects, we get the commutative diagram below.
\begin{center}
\begin{tikzcd}
A \ar[rd, "f"] \ar[rr, dashed, "0"] \ar[dd, "\img f"', two heads] && C \\
A \ar[rd, "f"] \ar[rr, dashed, "0"] \ar[dd, "\img f"', surjective head] && C \\
& B \ar[ru, "g"] \\
\Img f \ar[ru, hook, "\iota"] \ar[rr, dashed, "\exists!"] &&
\Ker g \ar["0"', dashed, uu] \ar[lu, hook']
Expand Down Expand Up @@ -284,10 +284,10 @@ \section{The Freyd-Mitchell embedding theorem}
\begin{tikzcd}
0 \ar[r]
& A \ar[r, hook, "p"] \ar[d, "\alpha", "\cong"']
& B \ar[r, two heads, "q"] \ar[d, "\beta"]
& B \ar[r, surjective head, "q"] \ar[d, "\beta"]
& C \ar[r] \ar[d, "\gamma", "\cong"']
& 0 \\
0 \ar[r] & A' \ar[r, hook, "p'"'] & B' \ar[r, two heads, "q'"'] & C' \ar[r] & 0
0 \ar[r] & A' \ar[r, hook, "p'"'] & B' \ar[r, surjective head, "q'"'] & C' \ar[r] & 0
\end{tikzcd}
\end{center}
and assume the top and bottom rows are exact.
Expand Down Expand Up @@ -382,7 +382,7 @@ \section{Breaking long exact sequences}
In an abelian category, consider the commutative diagram
\begin{center}
\begin{tikzcd}
A \ar[r, "p"] \ar[d, "\alpha"', two heads]
A \ar[r, "p"] \ar[d, "\alpha"', surjective head]
& B \ar[r, "q"] \ar[d, "\beta"', hook]
& C \ar[r, "r"] \ar[d, "\gamma"']
& D \ar[d, "\delta"', hook] \\
Expand Down Expand Up @@ -421,7 +421,7 @@ \section{Breaking long exact sequences}
In an abelian category, consider the commutative diagram
\begin{center}
\begin{tikzcd}
A \ar[r, "p"] \ar[d, "\alpha"', two heads]
A \ar[r, "p"] \ar[d, "\alpha"', surjective head]
& B \ar[r, "q"] \ar[d, "\beta"', "\cong"]
& C \ar[r, "r"] \ar[d, "\gamma"']
& D \ar[r, "s"] \ar[d, "\delta"', "\cong"]
Expand All @@ -441,7 +441,7 @@ \section{Breaking long exact sequences}
In an abelian category, consider the diagram
\begin{center}
\begin{tikzcd}
& A \ar[r, "f"] \ar[d, "a"] & B \ar[r, "g", two heads] \ar[d, "b"] & C \ar[r] \ar[d, "c"] & 0 \\
& A \ar[r, "f"] \ar[d, "a"] & B \ar[r, "g", surjective head] \ar[d, "b"] & C \ar[r] \ar[d, "c"] & 0 \\
0 \ar[r] & A' \ar[r, hook, "f'"'] & B' \ar[r, "g'"'] & C'
\end{tikzcd}
\end{center}
Expand Down
26 changes: 13 additions & 13 deletions tex/cats/categories.tex
View file
Original file line number Diff line number Diff line change
Expand Up @@ -345,7 +345,7 @@ \section{Binary products}
\begin{center}
\begin{tikzcd}
& X \\
X \times Y \ar[ru, two heads, "\pi_X"] \ar[rd, two heads, "\pi_Y"'] & \\
X \times Y \ar[ru, surjective head, "\pi_X"] \ar[rd, surjective head, "\pi_Y"'] & \\
& Y
\end{tikzcd}
\end{center}
Expand All @@ -365,7 +365,7 @@ \section{Binary products}
\begin{tikzcd}
&&& X \\
A \ar[rrru, bend left, "g"'] \ar[rrrd, bend right, "h"] \ar[rr, dotted, "\exists! f"] &&
X \times Y \ar[ru, two heads, "\pi_X"] \ar[rd, two heads, "\pi_Y"] & \\
X \times Y \ar[ru, surjective head, "\pi_X"] \ar[rd, surjective head, "\pi_Y"] & \\
&&& Y
\end{tikzcd}
\end{center}
Expand Down Expand Up @@ -404,9 +404,9 @@ \section{Binary products}
\begin{tikzcd}
& & X & & \\
\\
P_1 \ar[rrdd, "\pi_Y^1"', two heads] \ar[rruu, "\pi_X^1", two heads] \ar[rr, "f", two heads]
&& P_2 \ar[rr, "g", two heads] \ar[uu, "\pi_X^2"', two heads] \ar[dd, "\pi_Y^2", two heads]
&& P_1 \ar[lluu, "\pi_X^1"', two heads] \ar[lldd, "\pi_Y^1"', two heads] \\
P_1 \ar[rrdd, "\pi_Y^1"', surjective head] \ar[rruu, "\pi_X^1", surjective head] \ar[rr, "f", surjective head]
&& P_2 \ar[rr, "g", surjective head] \ar[uu, "\pi_X^2"', surjective head] \ar[dd, "\pi_Y^2", surjective head]
&& P_1 \ar[lluu, "\pi_X^1"', surjective head] \ar[lldd, "\pi_Y^1"', surjective head] \\
\\
&& Y &&
\end{tikzcd}
Expand Down Expand Up @@ -482,17 +482,17 @@ \section{Binary products}
\begin{tikzcd}
&& A
\ar[dd, "\exists! f"]
\ar[llddd, two heads, bend right]
\ar[lddd, two heads, bend right]
\ar[rddd, two heads, bend left]
\ar[rrddd, two heads, bend left]
\ar[llddd, surjective head, bend right]
\ar[lddd, surjective head, bend right]
\ar[rddd, surjective head, bend left]
\ar[rrddd, surjective head, bend left]
&& \\
&&&& \\
&& P
\ar[lld, two heads]
\ar[ld, two heads]
\ar[rd, two heads]
\ar[rrd, two heads]
\ar[lld, surjective head]
\ar[ld, surjective head]
\ar[rd, surjective head]
\ar[rrd, surjective head]
&& \\
X_1 & X_2 && X_3 & X_4
\end{tikzcd}
Expand Down
10 changes: 5 additions & 5 deletions tex/homology/cellular.tex
View file
Original file line number Diff line number Diff line change
Expand Up @@ -123,22 +123,22 @@ \section{Cellular chain complex}
\begin{tikzcd}[column sep=tiny]
& \underbrace{H_3(X^2)}_{=0} \ar[d, "0"] \\
\CX{4} \ar[r, "\partial_4"] \ar[rd, "d_4", blue]
& H_3(X^3) \ar[r, two heads] \ar[d, "0"]
& H_3(X^3) \ar[r, surjective head] \ar[d, "0"]
& \underbrace{H_3(X^4)}_{\cong H_3(X)} \ar[r, "0"]
& \underbrace{H_3(X^4, X^3)}_{= 0} \\
& \CX{3} \ar[d, "\partial_3"] \ar[rd, "d_3", blue]
&& \underbrace{H_1(X^0)}_{=0} \ar[d, "0"] \\
\underbrace{H_2(X^1)}_{=0} \ar[r, "0"]
& H_2(X^2) \ar[r, hook] \ar[d, two heads]
& H_2(X^2) \ar[r, hook] \ar[d, surjective head]
& \CX{2} \ar[r, "\partial_2"] \ar[rd, "d_2", blue]
& H_1(X^1) \ar[r, two heads]
& H_1(X^1) \ar[r, surjective head]
& \underbrace{H_1(X^2)}_{\cong H_1(X)} \ar[r, "0"]
& \underbrace{H_1(X^2, X^1)}_{=0} \\
& \underbrace{H_2(X^3)}_{\cong H_2(X)} \ar[d, "0"]
&& \CX{1} \ar[d, "\partial_1"] \ar[rd, "d_1", blue] \\
& \underbrace{H_2(X^3, X^2)}_{=0}
& \underbrace{H_0(\varnothing)}_{=0} \ar[r, "0"]
& H_0(X^0) \ar[r, hook] \ar[d, two heads]
& H_0(X^0) \ar[r, hook] \ar[d, surjective head]
& \CX{0} \ar[r, "\partial_0"]
& \dots \\
&&& \underbrace{H_0(X^1)}_{\cong H_0(X)} \ar[d, "0"] \\
Expand Down Expand Up @@ -210,7 +210,7 @@ \section{Cellular chain complex}
\begin{center}
\begin{tikzcd}
\underbrace{H_2(X^1)}_{=0} \ar[r, "0"] & H_2(X^2) \ar[r, hook] &
H_2(X^2, X^1) \ar[r, "\partial_2"] & H_1(X^1) \ar[r, two heads] &
H_2(X^2, X^1) \ar[r, "\partial_2"] & H_1(X^1) \ar[r, surjective head] &
\underbrace{H_1(X^2)}_{\cong H_1(X)} \ar[r, "0"]
& \underbrace{H_1(X^2, X^1)}_{=0}
\end{tikzcd}
Expand Down
24 changes: 12 additions & 12 deletions tex/homology/long-exact.tex
View file
Original file line number Diff line number Diff line change
Expand Up @@ -27,17 +27,17 @@ \section{Short exact sequences and four examples}
& \vdots \ar[d, "\partial_A"] & \vdots \ar[d, "\partial_B"] & \vdots \ar[d, "\partial_C"] & \\
0 \ar[r]
& A_{n+1} \ar[hook, r, "f_{n+1}"] \ar[d, "\partial_A"]
& B_{n+1} \ar[r, two heads, "g_{n+1}"] \ar[d, "\partial_B"]
& B_{n+1} \ar[r, surjective head, "g_{n+1}"] \ar[d, "\partial_B"]
& C_{n+1} \ar[r] \ar[d, "\partial_C"]
& 0 \\
0 \ar[r]
& A_n \ar[hook, r, "f_n"] \ar[d, "\partial_A"]
& B_n \ar[r, two heads, "g_n"] \ar[d, "\partial_B"]
& B_n \ar[r, surjective head, "g_n"] \ar[d, "\partial_B"]
& C_n \ar[r] \ar[d, "\partial_C"]
& 0 \\
0 \ar[r]
& A_{n-1} \ar[hook, r, "f_{n-1}"] \ar[d, "\partial_A"]
& B_{n-1} \ar[r, two heads, "g_{n-1}"] \ar[d, "\partial_B"]
& B_{n-1} \ar[r, surjective head, "g_{n-1}"] \ar[d, "\partial_B"]
& C_{n-1} \ar[r] \ar[d, "\partial_C"]
& 0 \\
& \vdots & \vdots & \vdots
Expand All @@ -52,7 +52,7 @@ \section{Short exact sequences and four examples}
For each $n$ consider
\begin{center}
\begin{tikzcd}[row sep=tiny]
C_n(U \cap V) \ar[r, hook] & C_n(U) \oplus C_n(V) \ar[r, two heads] & C_n(U + V) \\
C_n(U \cap V) \ar[r, hook] & C_n(U) \oplus C_n(V) \ar[r, surjective head] & C_n(U + V) \\
c \ar[r, mapsto] & (c, -c) \\
& (c, d) \ar[r, mapsto] & c + d
\end{tikzcd}
Expand All @@ -71,8 +71,8 @@ \section{Short exact sequences and four examples}
\begin{center}
\begin{tikzcd}[row sep=large]
0 \ar[r]
& C_0(U \cap V) \ar[r, hook] \ar[d, "\eps"', two heads]
& C_0(U) \oplus C_0(V) \ar[r, two heads] \ar[d, "\eps \oplus \eps"', two heads]
& C_0(U \cap V) \ar[r, hook] \ar[d, "\eps"', surjective head]
& C_0(U) \oplus C_0(V) \ar[r, surjective head] \ar[d, "\eps \oplus \eps"', surjective head]
& C_0(U+V) \ar[r] \ar[d, "\eps"']
& 0 \\
0 \ar[r]
Expand Down Expand Up @@ -105,8 +105,8 @@ \section{Short exact sequences and four examples}
\begin{center}
\begin{tikzcd}
0 \ar[r]
& C_0(A) \ar[r, hook] \ar[d, "\eps", two heads]
& C_0(X) \ar[r, two heads] \ar[d, "\eps", two heads]
& C_0(A) \ar[r, hook] \ar[d, "\eps", surjective head]
& C_0(X) \ar[r, surjective head] \ar[d, "\eps", surjective head]
& C_0(X,A) \ar[r]
& 0 \\
0 \ar[r] & \ZZ \ar[r, "\id"'] & \ZZ \ar[r] & 0 \ar[r] & 0.
Expand Down Expand Up @@ -162,8 +162,8 @@ \section{The long exact sequence of homology groups}
Recall that $H_n$ is ``cycles modulo boundaries'', and consider the sub-diagram
\begin{center}
\begin{tikzcd}
& B_n \ar[r, "g_n", two heads] \ar[d, "\partial_B"'] & C_n \ar[d, "\partial_C"] \\
A_{n-1} \ar[r, "f_{n-1}"', hook] & B_{n-1} \ar[r, "g_{n-1}"', two heads] & C_{n-1}
& B_n \ar[r, "g_n", surjective head] \ar[d, "\partial_B"'] & C_n \ar[d, "\partial_C"] \\
A_{n-1} \ar[r, "f_{n-1}"', hook] & B_{n-1} \ar[r, "g_{n-1}"', surjective head] & C_{n-1}
\end{tikzcd}
\end{center}
We need to take every cycle in $C_n$ to a cycle in $A_{n-1}$.
Expand Down Expand Up @@ -560,9 +560,9 @@ \section{The Mayer-Vietoris sequence}
\ii There is an isomorphism from $B$ to $A \oplus C$ such that the diagram
\begin{center}
\begin{tikzcd}
&& B \ar[rd, "g", two heads] \ar[dd, leftrightarrow, "\cong"] \\
&& B \ar[rd, "g", surjective head] \ar[dd, leftrightarrow, "\cong"] \\
0 \ar[r] & A \ar[ru, hook, "f"] \ar[rd, hook] && C \ar[r] & 0 \\
&& A \oplus C \ar[ru, two heads]
&& A \oplus C \ar[ru, surjective head]
\end{tikzcd}
\end{center}
commutes. (The maps attached to $A \oplus C$ are the obvious ones.)
Expand Down
6 changes: 5 additions & 1 deletion tex/preamble.tex
View file
Original file line number Diff line number Diff line change
Expand Up @@ -71,7 +71,11 @@
arrow style=tikz,
diagrams={>={Latex}},
tikzcd left hook/.tip={xGlyph[glyph math command=supset, swap, glyph axis = 5.7pt]},
tikzcd right hook/.tip={xGlyph[glyph math command=supset, glyph axis = 5.7pt]}
tikzcd right hook/.tip={xGlyph[glyph math command=supset, glyph axis = 5.7pt]},
surjective head arrow /.tip = {tikzcd to[sep=-1.5pt]tikzcd to},
surjective head/.style={
-surjective head arrow
}
}

%%fakesection Page layout
Expand Down
2 changes: 1 addition & 1 deletion tex/rep-theory/semisimple.tex
View file
Original file line number Diff line number Diff line change
Expand Up @@ -63,7 +63,7 @@ \section{Schur's lemma continued}
by the $mn$ choices of compositions
\begin{center}
\begin{tikzcd}
V \ar[r, hook] & V^{\oplus m} \ar[r, "T"] & V^{\oplus n} \ar[r, two heads] & V
V \ar[r, hook] & V^{\oplus m} \ar[r, "T"] & V^{\oplus n} \ar[r, surjective head] & V
\end{tikzcd}
\end{center}
where the first arrow is inclusion to the $i$th component of $V^{\oplus m}$
Expand Down

0 comments on commit 32cde85

Please sign in to comment.