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)