A locally cartesian closed functor is a functor between locally cartesian closed categories that preserves the locally cartesian closed structure up to coherent isomorphism.
cartesian closed category, locally cartesian closed category
cartesian closed functor, locally cartesian closed functor
cartesian closed model category, locally cartesian closed model category
cartesian closed (∞,1)-categorylocally cartesian closed (∞,1)-category
Elephant C3.3.1
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