Sentence examples for relative categories from inspiring English sources

Unfortunately, the choice is not always possible for example, many relative categories needed in applications do not satisfy Definition 2.6 (i).

A functor between relative categories (langle mathcal {C},W rangle ), (mathcal {C}',W' rangle ) is a functor (F:mathcal {C}rightarrow mathcal {C}') such that (F w) in W') for any (w in W).

The hazard estimates can the grouped into three relative categories for bedrock level accelerations greater than 0.21 g, 0.19 g, less than 0.16 g defining high, moderate, and low hazard levels, respectively.

Any functor (F:langle mathcal {C},W rangle rightarrow langle mathcal {C}',W' rangle ) between localizable relative categories induces a functor begin{aligned} {text {Ho}}(F):{text {Ho}}(mathcal {C},W) rightarrow {text {Ho}}(mathcal {C}',W').

A functor (Phi :langle mathcal {C}_0,W_0 rangle rightarrow langle mathcal {C}_1,W_1 rangle ) between two relative categories with model structures (C_0,F_0) and (C_1,F_1) is left-derivable if it sends morphisms in (C_0) to morphisms in (C_1) and morphisms in (C_0 cap W_0) to morphisms in (C_1 cap W_1).

In the second- and third-degree relative categories, there were 9742 grandparental, 2709 avuncular and 4 cousin pairs.

Let be the relative category of in.

Flat is a relative category that depends on the scale.

A model category is a saturated relative category equipped with a model structure.

Then (langle mathcal {C},{{text {Iso}}}rangle ) is a saturated relative category.

Assume given a pointed relative category (langle mathcal {C},W rangle ) equipped with a model structure.