Sentence examples for arbitrary sums from inspiring English sources

The functor e has a right-adjoint functor (e^dagger ), thus commutes with arbitrary sums, and then since e is conservative, this implies that h also commutes with arbitrary sums.

Since (C_cdot ({text {Ab}})) has arbitrary sums, so does the category ({text {DCoalg}}(C_cdot ({text {Ab}}),Q)).

Since (mathsf{Ind},mathcal {C}_0 rightarrow mathsf{Ind},mathcal {C}) commutes with arbitrary colimits, e commutes with arbitrary sums.

The category (mathsf{StHom}) has arbitrary sums, and it has the following remarkable property: for any triangulated category ({mathcal {D}}) with arbitrary sums, a triangulated functor (nu :mathsf{StHom}rightarrow {mathcal {D}}) that commutes with arbitrary sums admits a right-adjoint (nu ^dagger ) (this is a part of Brown Representability Theorem).

This argument can be quite powerful if one is independently motivated to deny arbitrary sums, and goes along with denying Unrestricted Mereology.

end{aligned} (10.9)In general, the functor (10.8) is triangulated, and it commutes with arbitrary sums, so it admits a right-adjoint functor (H^dagger ) by Brown representability.

At your fair price, you should be indifferent between taking either side.[6] de Finetti speaks of "an arbitrary sum" as the prize of the bet on E. The sum had better be potentially infinitely divisible, or else probability measurements will be precise only up to the level of 'grain' of the potential prizes.

The geographic boundaries are somewhat arbitrary, and summing total emissions to air within a region does not account for the movement of air across boundaries from nearby sources, or long range transport from distant sources.

Instead, the message was to keep going and try to get the sum over £1,000, an arbitrary amount chosen after the first few bets were won.

For instance, we have said that overlap may be a natural option if one is unwilling to countenance arbitrary scattered sums.

Then a believer in arbitrary mereological sums takes the relevant biconditional to the true, perhaps even necessarily so, although the predicate P is not distributive.