Sentence examples for the initial object from inspiring English sources

This is defined as the union of a class of sets containing the empty set (the initial object in the category of sets) and closed under the power-set operation and under transfinite unions thus, as a subcategory of the category of sets.

This so-called free topos has been constructed linguistically to satisfy any formalist, but it should also satisfy a moderate Platonist, one who is willing to abandon the principle of the excluded third, inasmuch as the free topos is the initial object in the category of all topoi.

We define the initial object likelihoods L k ∗, 0 as the saliency likelihoods.

4. The initial object pose is assumed to be the canonical one.

Therefore we can replace I with the category I(i) and assume that (i in I) is the initial object.

For the same experimental setting, we used the initial object pixels and background pixels (in Step 2, as shown in Figure 2) as the input of CRF.

The initial objects already specified are Endpoint, Structure, Structure Identifiers, Feature Definition, Feature, Feature Service, Reference, Algorithm, Algorithm Type, Model, Dataset, Validation Result, Applicability Domain, Feature Selection, and Reporting.

In addition, the empty set is the only initial object.

We can also restrict the Grothendieck cofibration (pi ) and the functor (7.10) to (M(I) subset (Delta ^L_M ^perp ) and obtain functors begin{aligned} pi :M(I) rightarrow Delta ^o, qquad rho :M(I) rightarrow I. end{aligned} (7.12 Since the normalization of a diagram (5.3) has the same initial object (i_0), we have (rho circ N cong rho ).

The address values point at the initial referent (object permanence, "Object permanence by using address").

This paper defines the recognition process as a sequential decision problem with the objective to disambiguate initial object hypotheses.