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Nil123
Nil123
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Consider the following pushout diagram $\require{AMScd}$ \begin{CD} A @>f>> B\\ @V g V V @VV V\\ C @>> > D \end{CD} in the category of $\textbf{Rings}$ where $f,g$ both are flat monomorphisms. The diagram is also a pullback diagram.

I'm trying to prove itshow that it's a pullback diagram but could not.

Consider the following pushout diagram $\require{AMScd}$ \begin{CD} A @>f>> B\\ @V g V V @VV V\\ C @>> > D \end{CD} in the category of $\textbf{Rings}$ where $f,g$ both are flat monomorphisms. The diagram is also a pullback diagram.

I'm trying to prove it but could not.

Consider the following pushout diagram $\require{AMScd}$ \begin{CD} A @>f>> B\\ @V g V V @VV V\\ C @>> > D \end{CD} in the category of $\textbf{Rings}$ where $f,g$ both are flat monomorphisms. The diagram is also a pullback diagram.

I'm trying to show that it's a pullback diagram but could not.

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Nil123
Nil123
  • 31
  • 3

Consider the following pushout diagram $\require{AMScd}$ \begin{CD} A @>f>> B\\ @V g V V @VV V\\ C @>> > D \end{CD} in the category of $\textbf{Rings}$ where $f,g$ both are flat monomorphisms. Is it possible that theThe diagram is also a pullback diagram?.

I'm trying to prove it but could not.

Consider the following pushout diagram $\require{AMScd}$ \begin{CD} A @>f>> B\\ @V g V V @VV V\\ C @>> > D \end{CD} in the category of $\textbf{Rings}$ where $f,g$ both are flat monomorphisms. Is it possible that the diagram is also a pullback diagram?

Consider the following pushout diagram $\require{AMScd}$ \begin{CD} A @>f>> B\\ @V g V V @VV V\\ C @>> > D \end{CD} in the category of $\textbf{Rings}$ where $f,g$ both are flat monomorphisms. The diagram is also a pullback diagram.

I'm trying to prove it but could not.

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Nil123
Nil123
  • 31
  • 3

Pushout and pullback in the category of rings

Consider the following pushout diagram $\require{AMScd}$ \begin{CD} A @>f>> B\\ @V g V V @VV V\\ C @>> > D \end{CD} in the category of $\textbf{Rings}$ where $f,g$ both are flat monomorphisms. Is it possible that the diagram is also a pullback diagram?