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The $(\Pi,\lambda)$-structures on the C-systems defined by universe categories
Theory and applications of categories, Tome 32 (2017), pp. 113-121 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

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Classification : 03F50, 18C50, 03B15, 18D15
Keywords: Type theory, Contextual category, Universe category, dependent product, product of families of types 
@article{TAC_2017_32_a3,
     author = {Vladimir Voevodsky},
     title = {The $(\Pi,\lambda)$-structures on the {C-systems} defined by universe categories},
     journal = {Theory and applications of categories},
     pages = {113--121},
     year = {2017},
     volume = {32},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a3/}
}
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Vladimir Voevodsky. The $(\Pi,\lambda)$-structures on the C-systems defined by universe categories. Theory and applications of categories, Tome 32 (2017), pp. 113-121. http://geodesic.mathdoc.fr/item/TAC_2017_32_a3/