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<span class="kw">consider </span><font color="Maroon" title="c6">D</font> being   <a href="cat_6.html#V1" title="CAT_6:attr.1">strict</a>  <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a>, <font color="Maroon" title="c7">P1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c6">D</font>,<font color="Maroon" title="c2">C1</font>, <font color="Maroon" title="c8">P2</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Maroon" title="c6">D</font>,<font color="Maroon" title="c3">C2</font><span class="kw"> such that </span><br/><a NAME="E2:84_1_1"/><span class="lab"><font color="Green" title="E47">A3</font></span>: 
(  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c6">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">f1</font>,<font color="Olive" title="b2">f2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">f1</font> is   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <font color="Maroon" title="c2">C1</font>, <font color="Olive" title="b2">f2</font> is   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <font color="Maroon" title="c3">C2</font> : ( <font color="Olive" title="b1">f1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C1</font> &amp; <font color="Olive" title="b2">f2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">C2</font> &amp; <font color="Maroon" title="c4">F1</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b1">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F2</font> <a href="cat_6.html#K9" title="CAT_6:func.9">.</a> <font color="Olive" title="b2">f2</font> ) </span> } </span>  &amp;  the <a href="cat_6.html#U1" title="CAT_6:sel.1">composition</a> of <font color="Maroon" title="c6">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">f1</font>,<font color="Olive" title="b2">f2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b3">f3</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> where <font color="Olive" title="b1">f1</font>, <font color="Olive" title="b2">f2</font>, <font color="Olive" title="b3">f3</font> is   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <font color="Maroon" title="c6">D</font> : ( <font color="Olive" title="b1">f1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c6">D</font> &amp; <font color="Olive" title="b2">f2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c6">D</font> &amp; <font color="Olive" title="b3">f3</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c6">D</font> &amp; (  for <font color="Olive" title="b4">f11</font>, <font color="Olive" title="b5">f12</font>, <font color="Olive" title="b6">f13</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <font color="Maroon" title="c2">C1</font><br/>  for <font color="Olive" title="b7">f21</font>, <font color="Olive" title="b8">f22</font>, <font color="Olive" title="b9">f23</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <font color="Maroon" title="c3">C2</font>  st <font color="Olive" title="b1">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b4">f11</font>,<font color="Olive" title="b7">f21</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b2">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b5">f12</font>,<font color="Olive" title="b8">f22</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b3">f3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b6">f13</font>,<font color="Olive" title="b9">f23</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/>( <font color="Olive" title="b4">f11</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Olive" title="b5">f12</font> &amp; <font color="Olive" title="b7">f21</font> <a href="cat_6.html#NR2" title="CAT_6:NR.2">|&gt;</a> <font color="Olive" title="b8">f22</font> &amp; <font color="Olive" title="b6">f13</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">f11</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Olive" title="b5">f12</font> &amp; <font color="Olive" title="b9">f23</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">f21</font> <a href="cat_6.html#K2" title="CAT_6:func.2">(*)</a> <font color="Olive" title="b8">f22</font> ) ) ) </span> } </span>  &amp; <font color="Maroon" title="c7">P1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c8">P2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Maroon" title="c6">D</font>,<font color="Maroon" title="c7">P1</font>,<font color="Maroon" title="c8">P2</font> <a href="cat_7.html#R3" title="CAT_7:pred.3">is_pullback_of</a> <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:84"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="txt" href="#E2:84"><span class="lab"><font color="Green" title="E46">A2</font></span></a>, <a class="ref" href="cat_7.html#T51" target="_self" onmouseover="rs('cat_7/T51')" onmouseout="rh()">Th51</a></span>;<br/>
<span class="kw">take </span>
<span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Maroon" title="c6">D</font>,<font color="Maroon" title="c7">P1</font>,<font color="Maroon" title="c8">P2</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">D</font> being   <a href="cat_6.html#V1" title="CAT_6:attr.1">strict</a>  <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a> ex <font color="Olive" title="b2">P1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D</font>,<font color="Maroon" title="c2">C1</font> ex <font color="Olive" title="b3">P2</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D</font>,<font color="Maroon" title="c3">C2</font> st <br/>( <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Maroon" title="c6">D</font>,<font color="Maroon" title="c7">P1</font>,<font color="Maroon" title="c8">P2</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Olive" title="b1">D</font>,<font color="Olive" title="b2">P1</font>,<font color="Olive" title="b3">P2</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> &amp; <font color="Olive" title="b2">P1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b3">P2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b1">D</font>,<font color="Olive" title="b2">P1</font>,<font color="Olive" title="b3">P2</font> <a href="cat_7.html#R3" title="CAT_7:pred.3">is_pullback_of</a> <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> )</span><br/>

<span class="kw">thus </span><a NAME="E3:84_1_1"/>
 ex <font color="Olive" title="b1">D</font> being   <a href="cat_6.html#V1" title="CAT_6:attr.1">strict</a>  <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a> ex <font color="Olive" title="b2">P1</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D</font>,<font color="Maroon" title="c2">C1</font> ex <font color="Olive" title="b3">P2</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">D</font>,<font color="Maroon" title="c3">C2</font> st <br/>( <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Maroon" title="c6">D</font>,<font color="Maroon" title="c7">P1</font>,<font color="Maroon" title="c8">P2</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><font color="Olive" title="b1">D</font>,<font color="Olive" title="b2">P1</font>,<font color="Olive" title="b3">P2</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> &amp; <font color="Olive" title="b2">P1</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b3">P2</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b1">D</font>,<font color="Olive" title="b2">P1</font>,<font color="Olive" title="b3">P2</font> <a href="cat_7.html#R3" title="CAT_7:pred.3">is_pullback_of</a> <font color="Maroon" title="c4">F1</font>,<font color="Maroon" title="c5">F2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:84_1_1"><span class="lab"><font color="Green" title="E47">A3</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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