inclusion functor造句

• The construction of " R " ^ given above yields a left adjoint to the inclusion functor.
• The inclusion functor has a left adjoint and that is exactly F \ mapsto \ pi _ 0 F.
• The abelianization functor is the left adjoint of the inclusion functor from the category of abelian groups to the category of groups.
• Here is an explicit example of a full, additive subcategory of an abelian category which is itself abelian but the inclusion functor is not exact.
• Then each \ mathbf A _ n is an abelian category and we have an inclusion functor I \ colon \ mathbf A _ 2 \ to \ mathbf A _ 3 identifying the simple projective, simple injective and indecomposable projective-injective modules.
• The existence of the abelianization functor "'Grp "'?! "'Ab "'makes the category Ab a reflective subcategory of the category of groups, defined as a full subcategory whose inclusion functor has a left adjoint.
• This main result is completed by the observation that for the functor pt o & Omega;, sending each space to the points of its open set lattice is left adjoint to the inclusion functor from "'Sob "'to "'Top " '.