Here I add notes about notation I use in this blog.
- I might use the notion of fibered category and category fibered in groupoids as if there is no difference. I am mostly interested in fibered category \(\mathcal{F}\rightarrow \mathcal{C}\) where the fibre \(\mathcal{F}(U)\) is a groupoid for every object \(U\) of \(\mathcal{C}\). So, most of the times when I say fibered category, it is most likely that I mean fibred categroy whose fibres are groupoids i.e., category fibered in groupoids. Please let me know if there is some real confusion.