Welcome to the section of the Around toposes Forum specifically devoted to discussions on the role of toposes as unifying 'bridges' across different mathematical theories. Feel free to ask questions on any aspect of these general methodologies. 

Please note that the forum has built-in latex editors for writing mathematical formulas; if you write

for each latex expression you need to insert, it will be automatically displayed inside a blank box (you can check the result by clicking on the Preview button).

You can also, for a better graphical result, just type as if you were writing a normal latex text, but beware that in that case the Preview button will not show the compiled result (still, you will be able to edit your message for 60 minutes after your original submission, in particular to correct any typos or rendering mistakes). Here is an example:

$\textup{Hom}_{[{\cal C}^{\textup{op}}, \textbf{Set}]}(y_{{\cal C}}(c),F)≅F(c).$

We look forward to hearing from you!