Updated the Functor images

categories.html

@@ -304,7 +304,6 @@ A <em>functor</em> \(\F\) from \(\C\) to \(\D\):</p>
 <div style="position:relative">
 <img src="img/mp/functor.png" alt="Functor" style="position:absolute;left:0;top:0"/>
 <img class="slide" src="img/mp/functor-morphism.png" alt="Functor Morphisms" style="position:absolute;left:0;top:0"/>
-<img class="slide" src="img/mp/functor-morphism2.png" alt="Functor Morphisms" style="position:absolute;left:0;top:0"/>
 <img class="slide" src="img/mp/functor-morphism-color.png" alt="Functor Morphisms" style="position:absolute;left:0;top:0"/>
 </div>
 </section>

categories/slide-019.html

@@ -3,6 +3,5 @@
 <div style="position:relative">
 <img src="img/mp/functor.png" alt="Functor" style="position:absolute;left:0;top:0"/>
 <img class="slide" src="img/mp/functor-morphism.png" alt="Functor Morphisms" style="position:absolute;left:0;top:0"/>
-<img class="slide" src="img/mp/functor-morphism2.png" alt="Functor Morphisms" style="position:absolute;left:0;top:0"/>
 <img class="slide" src="img/mp/functor-morphism-color.png" alt="Functor Morphisms" style="position:absolute;left:0;top:0"/>
 </div>

img/mp/functor-morphism-color.mp

@@ -3,10 +3,9 @@ z1=(gu,0);
 z2=(.5gu,-.75gu);
 z3=z0 shifted (2gu,0);
 z4=z3 shifted (0,-.75gu);
-z5=.5[z1,z4] shifted (0,1gu);
-z6=z5 shifted (0,-1.8gu);
 
-draw z5--z6 withpen pencircle scaled 1.3bp dashed evenly;
+drawblock(z0,(xpart z1,ypart z2),btex $\mathcal{C}$ etex);
+drawblock(z3,z4,btex $\mathcal{D}=\mathbf{F}(\mathcal{C})$ etex);
 
 drawoptions(withcolor yellow );
 drawState(z0,btex $A$ etex);
@@ -17,18 +16,22 @@ drawoptions(withcolor red);
 drawState(z2,btex $C$ etex);
 drawState(z4,btex $Y$ etex);
 
-drawoptions(withcolor blue);
-drawEdge(z0,z0,btex $id_A$ etex);
-drawEdge(z1,z1,btex $id_B$ etex);
-drawEdge(z3,z3,btex $id_X$ etex);
-drawarrow edgeAngle(z0,z1,35);
-drawarrow edgeAngle(z1,z0,-145);
 
 drawoptions(withcolor green );
 drawEdge(z2,z2,btex $id_C$ etex);
-drawEdge(z4,z4,btex $id_Y$ etex);
+
 
 drawoptions(withcolor magenta );
 drawarrow edgeTwoAngles(z1,z2,-90,180);
 drawarrow edgeTwoAngles(z0,z2,-90,0);
 drawarrow edgeTwoAngles(z3,z4,-35,35+180);
+
+drawoptions(withcolor blue );
+drawEdge(z0,z0,btex $id_A$ etex);
+drawEdge(z1,z1,btex $id_B$ etex);
+drawarrow edgeAngle(z0,z1,35);
+drawarrow edgeAngle(z1,z0,-145);
+drawEdge(z3,z3,btex $id_X$ etex);
+
+drawoptions(withcolor green );
+drawEdge(z4,z4,btex $id_Y$ etex);

img/mp/functor-morphism.mp

@@ -4,31 +4,35 @@ z2=(.5gu,-.75gu);
 z3=z0 shifted (2gu,0);
 z4=z3 shifted (0,-.75gu);
 
-drawblock(z0,(xpart z1,ypart z2),btex $\mathbf{C}$ etex);
-drawblock(z3,z4,btex $\mathbf{D}$ etex);
+drawblock(z0,(xpart z1,ypart z2),btex $\mathcal{C}$ etex);
+drawblock(z3,z4,btex $\mathcal{D}=\mathbf{F}(\mathcal{C})$ etex);
 
 drawState(z0,btex $A$ etex);
 drawState(z1,btex $B$ etex);
 drawState(z2,btex $C$ etex);
 
+drawState(z4,btex $Y$ etex);
+drawState(z3,btex $X$ etex);
 
-drawEdge(z0,z0,btex $id_A$ etex);
-drawEdge(z1,z1,btex $id_B$ etex);
+
+drawoptions(withcolor green withpen pencircle scaled 1);
 drawEdge(z2,z2,btex $id_C$ etex);
-drawarrow edgeAngle(z0,z1,35);
-drawarrow edgeAngle(z1,z0,-145);
+
+
+drawoptions(withcolor magenta withpen pencircle scaled 1);
 drawarrow edgeTwoAngles(z1,z2,-90,180);
 drawarrow edgeTwoAngles(z0,z2,-90,0);
-
-drawoptions(withcolor blue);
-
-drawState(z3,btex $X$ etex);
-drawState(z4,btex $Y$ etex);
-drawEdge(z3,z3,btex $id_X$ etex);
-drawEdge(z4,z4,btex $id_Y$ etex);
 drawarrow edgeTwoAngles(z3,z4,-35,35+180);
 
-drawoptions(withcolor yellow);
+drawoptions(withcolor blue withpen pencircle scaled 1);
+drawEdge(z0,z0,btex $id_A$ etex);
+drawEdge(z1,z1,btex $id_B$ etex);
+drawarrow edgeAngle(z0,z1,35);
+drawarrow edgeAngle(z1,z0,-145);
+drawEdge(z3,z3,btex $id_X$ etex);
+
+drawoptions(withcolor green withpen pencircle scaled 1);
+drawEdge(z4,z4,btex $id_Y$ etex);
 
 % drawarrow edgeAngle(z0,z3,45);
 % drawarrow edge(z1,z3);
@@ -49,8 +53,41 @@ ix := midpoint( lx );
 iy := midpoint( ly );
 
 nodesize:= .5u;
-drawoptions(withcolor blue dashed evenly);
+drawoptions(withcolor blue dashed evenly withpen pencircle scaled 1);
 
 drawarrow edgeAngle(ia,ix,35);
 drawarrow edgeAngle(ib,ix,20);
-drawarrow edgeAngle(ic,iy,35);
+
+drawoptions(withcolor green dashed evenly withpen pencircle scaled 1);
+drawarrow edgeAngle(ic,iy,0);
+
+path f,g,h,i;
+f:= edgeAngle(z0,z1,35);
+g:= edgeAngle(z1,z0,-145);
+h:= edgeTwoAngles(z1,z2,-90,180);
+i:= edgeTwoAngles(z0,z2,-90,0);
+
+path k;
+k:= edgeTwoAngles(z3,z4,-35,35+180);
+
+pair mf,mg,mh,mi,mk;
+mf := midpoint(f);
+mg := midpoint(g);
+mh := midpoint(h);
+mi := midpoint(i);
+mk := midpoint(k);
+
+path lx,ly;
+lx := edge(z3,z3);
+ly := edge(z4,z4);
+pair ix,iy;
+ix := midpoint( lx );
+
+nodesize:= .5u;
+
+drawoptions(withcolor blue dashed evenly withpen pencircle scaled 1);
+drawarrow edgeAngle(mf,ix,35);
+drawarrow edgeAngle(mg,ix,-15);
+drawoptions(withcolor magenta dashed evenly withpen pencircle scaled 1);
+drawarrow edgeAngle(mi,mk,15);
+drawarrow edgeAngle(mh,mk,15);

img/mp/functor-morphism2.mp

@@ -1,61 +0,0 @@
-z0=(0,0); z1=(gu,0); z2=(.5gu,-.75gu);
-z3=z0 shifted (2gu,0);
-z4=z3 shifted (0,-.75gu);
-z5=.5[z1,z4] shifted (0,1gu);
-z6=z5 shifted (0,-1.8gu);
-
-draw z5--z6 withpen pencircle scaled 1.3bp dashed evenly;
-
-drawState(z0,btex $A$ etex);
-drawState(z1,btex $B$ etex);
-drawState(z2,btex $C$ etex);
-
-
-drawEdge(z0,z0,btex $id_A$ etex);
-drawEdge(z1,z1,btex $id_B$ etex);
-drawEdge(z2,z2,btex $id_C$ etex);
-
-path f,g,h,i;
-f:= edgeAngle(z0,z1,35);
-g:= edgeAngle(z1,z0,-145);
-h:= edgeTwoAngles(z1,z2,-90,180);
-i:= edgeTwoAngles(z0,z2,-90,0);
-
-drawarrow f;
-drawarrow g;
-drawarrow h;
-drawarrow i;
-
-drawoptions(withcolor blue);
-
-drawState(z3,btex $X$ etex);
-drawState(z4,btex $Y$ etex);
-drawEdge(z3,z3,btex $id_X$ etex);
-drawEdge(z4,z4,btex $id_Y$ etex);
-
-path k;
-k:= edgeTwoAngles(z3,z4,-35,35+180);
-drawarrow  k;
-
-
-drawoptions(withcolor yellow withpen pencircle scaled 1.3bp dashed evenly);
-
-pair mf,mg,mh,mi,mk;
-mf := midpoint(f);
-mg := midpoint(g);
-mh := midpoint(h);
-mi := midpoint(i);
-mk := midpoint(k);
-
-path lx,ly;
-lx := edge(z3,z3);
-ly := edge(z4,z4);
-pair ix,iy;
-ix := midpoint( lx );
-
-nodesize:= .5u;
-
-drawarrow edgeAngle(mf,ix,45);
-drawarrow edgeAngle(mg,ix,45);
-drawarrow edgeAngle(mi,mk,15);
-drawarrow edgeAngle(mh,mk,15);

img/mp/functor.mp

@@ -4,9 +4,8 @@ z2=(.5gu,-.75gu);
 z3=z0 shifted (2gu,0);
 z4=z3 shifted (0,-.75gu);
 
-drawblock(z0,(xpart z1,ypart z2),btex $\mathbf{C}$ etex);
-drawblock(z3,z4,btex $\mathbf{D}$ etex);
-
+drawblock(z0,(xpart z1,ypart z2),btex $\mathcal{C}$ etex);
+drawblock(z3,z4,btex $\mathcal{D}=\mathbf{F}(\mathcal{C})$ etex);
 
 drawEdge(z0,z0,btex $id_A$ etex);
 drawEdge(z1,z1,btex $id_B$ etex);