Sentence examples for opposite categories from inspiring English sources

In the second case, pass to the opposite categories.

For (U_dagger ), one does the same procedure with the opposite categories, restricting to (I_L) instead of (I_M).

By Remark 2.21, it suffices to consider the case of the left-derivable functor; for the right-derivable functor, everything then follows by passing to the opposite categories.

Passing to the opposite categories, we also see that in the assumptions of Lemma 7.3, (mathcal {C}^{I^o}) has a projective model structure in the sense of Definition 2.7.

To obtain the number of genes in opposite categories, two-fold change was used as criterion.

Furthermore, proportional model resulted in fewer genes in opposite categories than additive model.

But the Centre for Cities concluded that half the nation's cities fall into the opposite category of "low wages, high welfare".

The equivalent – if not precisely equal and opposite – category, "Bad Straight Art", is an alternately Gucci and gingham-clad arena, wherein the cultural artefact is venerated more for its loyalty to an antediluvian conception of gender difference than any intrinsic merit.

The opposite category ((Delta X)^o) is then also a Reedy category, with the opposite Reedy structure.

Then the opposite category (V(X)^o) is ordered, with the degree function given by cardinality.

Alternatively, one can send ([n] in Delta ) to the opposite category ([n]^o).