Reflective Subcategory
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a subcategory A of a category B is said to be reflective in B when the inclusion functor from A to B has a left adjoint. This adjoint is sometimes called a reflector. Dually, A is said to be coreflective in B when the inclusion functor has a right adjoint. All these notions are special case of the common generalization E-reflective subcategory, where E is a class of morphisms. The E-reflective hull of a class A of objects is defined as the smallest E-r...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a subcategory A of a category B is said to be reflective in B when the inclusion functor from A to B has a left adjoint. This adjoint is sometimes called a reflector. Dually, A is said to be coreflective in B when the inclusion functor has a right adjoint. All these notions are special case of the common generalization E-reflective subcategory, where E is a class of morphisms. The E-reflective hull of a class A of objects is defined as the smallest E-reflective subcategory containing A. Thus we can speak about reflective hull, epireflective hull, extremal epireflective hull, etc. Dual notions to the above mentioned notions are coreflection, coreflection arrow, (mono) coreflective subcategory, coreflective hull.
