Hello,

I read the paper on groupoid interpretation of type theory by Hofmann and Streicher and I have a question. According to the authors $Tm([[\text{Set}\:[\Gamma]\: ]])$ is the same as $\text{Se}([[\Gamma]])$ but I don't understand because an element of $Tm([[\text{Set}\,[\Gamma]\:]])$ is a pseudo-fonctor (from $[[\Gamma]]$ to GPD) as said page 10 while an element of $\text{Se}([[\Gamma]])$ is a true fonctor (from $[[\Gamma]]$ to Gpd). Have you an idea ?

Best

P.S: I precise that the paper I mention is entitled *The Groupoid Interpretation of Type Theory* by Martin Hofmann and Thomas Streicher. You can find this article here http://www.mathematik.tu-darmstadt.de/~streicher/
Thanks