Sentence examples for be the full subcategory from inspiring English sources

To obtain ({mathcal {D}}(mathcal {C})), one takes ({mathcal {D}}=H mathcal {C})), and lets ({mathcal {D}}') be the full subcategory spanned by acyclic complexes.

Let (I_{ge n'} subset I) be the full subcategory spanned by objects i such that (n' le deg (i)), and let (varepsilon :I_{ge n'} rightarrow I) be the embedding functor.

Consider the matching category M i) of the object (i in I) with its simplicial replacement (Delta M i)), and let (overline{Delta } M i) subset Delta M i)) be the full subcategory spanned by non-degenerate simplices.

Let (widetilde{mathcal {C}} subset widetilde{mathcal {C}}') be the full subcategory spanned by (mathcal {C}_0 subset mathcal {C}'_0) and (mathcal {C}_1 subset mathcal {C}'_1).

Assume given a stable model pair (langle mathcal {C},mathcal {C}' rangle ) and a full triangulated subcategory ({mathcal {D}}_0 subset {mathcal {D}}= {text {Ho}}(mathcal {C})), and let (mathcal {C}_0 subset mathcal {C}) be the full subcategory spanned by objects X with (h(X) in {mathcal {D}}_0).

Assume given a simplicial set X and a generating fibration (mathcal {C}' rightarrow Delta X), and let (mathcal {C}subset mathcal {C}') be the full subcategory spanned by the subcategories (mathcal {C}_c subset mathcal {C}'_c subset mathcal {c}'), (c in Delta X).

The matching expansion M(I) of the Reedy category I is the full subcategory (M(I) subset (Delta ^M_L I ^perp ) spanned by non-degenerate objects.

By definition, the fiber (M(I _i subset M(I)) is the full subcategory spanned by (langle [n],i_cdot rangle ) with (i_0=i).

The subcategory R ′ consists of all regular representations with no indecomposable direct summand in T ∞, or equivalently, it is the full subcategory of all representations M such that M α is bijective.

The reduction (R(mathcal {C})) of the normalized special prefibration (mathcal {C}) is the full subcategory (R(mathcal {C}) subset widetilde{R}(mathcal {C})) spanned by the essential images of the fully faithful functors (6.20).

A section of such a prefibration is special if it is cartesian along all special maps in the sense of Definition 4.5 (ii), and ({text {Sec}}_+(Delta X,mathcal {C}) subset {text {Sec}}(Delta X,mathcal {C})) is the full subcategory spanned by special sections.