Implication Details
Assumptions: cocomplete, extensive, locally cartesian closed
Conclusions: infinitary extensive
Reason: The pullback functor preserves coproducts because it has a right adjoint. See also Remark 2.6 at the nLab.
Assumptions: cocomplete, extensive, locally cartesian closed
Conclusions: infinitary extensive
Reason: The pullback functor preserves coproducts because it has a right adjoint. See also Remark 2.6 at the nLab.