0 a reduction in the amount of money that a company or person spends: --
1 a situation in which prices fall suddenly from a high level: --
Here we require that the category must be at least lex, since we want to interpret substitution via pullback.
Indeed, to interpret substitution, we need to find a canonical choice of pullbacks that is functorial and is strictly preserved by the categorical structure.
Then (1) is a pullback if and only if it satisfies the reduced chain-condition and f, g is monomorphic.
For the rest, we add as before the pullback tiles that provide the coordination mechanism about local instantiations.
Let us note a general 2-categorical fact, that pullback functors between slices preserve existing exponentials.
Techniques based on the pullback of differential forms are instrumental in getting interpolation estimates.
The gist of affine equivalence techniques is to use these estimates in combination with the pullback formulas (2.16)-(2.19) for vector proxies.
Let be a weak inclusive category that has pullbacks.
