Talk:Extranatural transformation

Diagrams

The diagrams are to small. Here is the LaTeX source:

\begin{Def}[Extranatural transformation] Let $F:A\times B^{op}\times B\rightarrow D$, $G:A\times C^{op}\times C\rightarrow D$ functors of Categories. \\A family $$\eta (a,b,c):F(a,b,b)\rightarrow G(a,c,c)$$ is said to be \em{natural in a and extranatural in b and c} if the following hold:
\begin{enumerate}
\item $\eta(-,b,c)$ is a natural transformation (in the usual sense).
\item (extranaturality in b) \\$\forall (g:b\rightarrow b^\prime)\in MorB$, $\forall a\in A$, $\forall c\in C$ the following diagram commutes
 $$\begin{CD}F(a,b,b^\prime)@>{F(1,1,g) }>>F(a,b,b)\\
@VF(1,g,1)VV&@V{\eta (a,b,c)}VV	\\
F(a,b^\prime,b^\prime)@>{\eta (a,b^\prime ,c )}>>G(a,c,c)\end{CD}$$
\item (extranaturality in c) \\$\forall (h:c\rightarrow c^\prime)\in MorC$, $\forall a\in A$, $\forall b\in B$ the following diagram commutes
 $$\begin{CD}F(a,b,b)@>{\eta(a,b,c) }>>G(a,c,c)\\
@V\eta (a,b,c^\prime)VV&@V{G (1,h,1)}VV	\\
G(a,c^\prime,c^\prime)@>{G (1,1,h )}>>G(a,c^\prime,c)\end{CD}$$
\end{enumerate}
\end{Def}

Stephan Spahn (talk) 14:06, 31 May 2011 (UTC)

I replaced the PDFs with TeX typeset in wiki standards. PDF files are now voted for deletion, please take action to remove them. Demmo (talk) 07:03, 1 June 2011 (UTC)