# The $(\Pi,\lambda)$-structures on the C-systems defined by universe categories

We define the notion of a $(P,\tilde{P})$-structure on a universe $p$ in a locally cartesian closed category category with a binary product structure and construct a $(\Pi,\lambda)$-structure on the C-systems $CC(C,p)$ from a $(P,\tilde{P})$-structure on $p$. We then define homomorphisms of C-systems with $(\Pi,\lambda)$-structures and functors of universe categories with $(P,\tilde{P})$-structures and show that our construction is functorial relative to these definitions.