Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more,
all in one place.
Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more,
all in one place.
| Download
GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346\begin{sequent}1\begin{align*}2a: \Obj, b: \Obj ~|~ () \vdash \IsZero \big( \ZeroMorphism( a, b ) \big)3\end{align*}4\end{sequent}56\begin{sequent}7\begin{align*}8a: \Obj, b: \Obj ~|~ () \vdash \IsIdenticalToZeroMorphism \big( \ZeroMorphism( a, b ) \big)9\end{align*}10\end{sequent}1112\begin{sequent}13\begin{align*}14a: \Obj ~|~ () \vdash \IsZero \big( \UniversalMorphismIntoZeroObject( a ) \big)15\end{align*}16\end{sequent}1718\begin{sequent}19\begin{align*}20a: \Obj ~|~ () \vdash \IsZero \big( \UniversalMorphismFromZeroObject( a ) \big)21\end{align*}22\end{sequent}2324\begin{sequent}25\begin{align*}26\alpha: \Mor ~|~ \IsZero(\Source(\alpha)) \vdash \IsZero(\alpha)27\end{align*}28\end{sequent}2930\begin{sequent}31\begin{align*}32\alpha: \Mor ~|~ \IsZero(\Range(\alpha)) \vdash \IsZero(\alpha)33\end{align*}34\end{sequent}3536\begin{sequent}37\begin{align*}38\alpha: \Mor ~|~ \IsZero(\alpha), \IsMonomorphism(\alpha) \vdash \IsZero(\Source(\alpha))39\end{align*}40\end{sequent}4142\begin{sequent}43\begin{align*}44\alpha: \Mor ~|~ \IsZero(\alpha), \IsEpimorphism(\alpha) \vdash \IsZero(\Range(\alpha))45\end{align*}46\end{sequent}4748\begin{sequent}49\begin{align*}50\alpha: \Mor, \beta: \Mor ~|~ \IsZero(\alpha) \vdash \IsZero(\PreCompose(\alpha,\beta))51\end{align*}52\end{sequent}5354\begin{sequent}55\begin{align*}56\alpha: \Mor, \beta: \Mor ~|~ \IsZero(\beta) \vdash \IsZero(\PreCompose(\alpha,\beta))57\end{align*}58\end{sequent}5960\begin{sequent}61\begin{align*}62\alpha: \Mor ~|~ \IsInitial\big( \KernelObject( \alpha ) \big) \vdash \IsMonomorphism( \alpha )63\end{align*}64\end{sequent}6566\begin{sequent}67\begin{align*}68\alpha: \Mor ~|~ \IsMonomorphism( \alpha ) \vdash \IsZero( \KernelObject( \alpha ) )69\end{align*}70\end{sequent}7172\begin{sequent}73\begin{align*}74\alpha: \Mor ~|~ \IsZero\big( \KernelEmbedding( \alpha ) \big) \vdash \IsMonomorphism( \alpha )75\end{align*}76\end{sequent}7778\begin{sequent}79\begin{align*}80\alpha: \Mor ~|~ \IsMonomorphism( \alpha ) \vdash \IsZero( \KernelEmbedding( \alpha ) )81\end{align*}82\end{sequent}8384\begin{sequent}85\begin{align*}86\alpha: \Mor ~|~ \IsTerminal\big( \CokernelObject( \alpha ) \big) \vdash \IsEpimorphism( \alpha )87\end{align*}88\end{sequent}8990\begin{sequent}91\begin{align*}92\alpha: \Mor ~|~ \IsEpimorphism( \alpha ) \vdash \IsZero\big( \CokernelObject( \alpha ) \big)93\end{align*}94\end{sequent}9596\begin{sequent}97\begin{align*}98\alpha: \Mor ~|~ \IsZero\big( \CokernelProjection( \alpha ) \big) \vdash \IsEpimorphism( \alpha )99\end{align*}100\end{sequent}101102\begin{sequent}103\begin{align*}104\alpha: \Mor ~|~ \IsEpimorphism( \alpha ) \vdash \IsZero\big( \CokernelProjection( \alpha ) \big)105\end{align*}106\end{sequent}107108109