More Formal Consequences Projection, Base Change

7 More Formal Consequences Projection, Base Change 

We give some additional consequences, to be used later, of the formalism in 3.6. Again, the introductory remarks in 3.4, suitably modified, are relevant. 

Condition (ii) there means that for / X — Y in S, we have functorial maps 

For X S, the product functor on the monoidal category X = X will be denoted by . 

Subdiagram commutes because of commutativity of (3.6.2) (see condition (iii) in (3.6.7)(d)), Subdiagram commutes because of the commutativity of (3.6.7.2) (which is part of the definition of monoidal pseudofunctor) and commutativity of the remaining subdiagrams is clear. The conclusion follows. 

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