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Functorial Factorization, Wellpointedness and Separability
"... A functorial treatment of factorization structures is presented, under extensive use of wellpointed endofunctors. Actually, socalled weak factorization systems are interpreted as pointed lax indexed endofunctors, and this sheds new light on the correspondence between reflective subcategories and f ..."
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A functorial treatment of factorization structures is presented, under extensive use of wellpointed endofunctors. Actually, socalled weak factorization systems are interpreted as pointed lax indexed endofunctors, and this sheds new light on the correspondence between reflective subcategories and factorization systems. The second part of the paper presents two important factorization structures in the context of pointed endofunctors: concordantdissonant and inseparableseparable.
SEVERAL CONSTRUCTIONS FOR FACTORIZATION SYSTEMS DALI ZANGURASHVILI
"... Abstract. The paper develops the previously proposed approach to constructing factorization systems in general categories. This approach is applied to the problem of finding conditions under which a functor (not necessarily admitting a right adjoint) "reflects"factorization system ..."
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Abstract. The paper develops the previously proposed approach to constructing factorization systems in general categories. This approach is applied to the problem of finding conditions under which a functor (not necessarily admitting a right adjoint) &quot;reflects&quot;factorization systems. In particular, a generalization of the wellknown CassidyH'ebertKelly factorization theorem is given. The problem of relating a factorization system toa pointed endofunctor is considered. Some relevant examples in concrete categories are given. 1. Introduction The problem of relating a factorization system on a category C to an adjunction C I / / XHoo, (1.1) was thoroughly considered by C. Cassidy, M. H'ebert and G. M. Kelly in [CHK]. The wellknown theorem of these authors states that in the case of a finitely wellcomplete category C the pair of morphism classes\Gamma
SEVERAL CONSTRUCTIONS FOR FACTORIZATION SYSTEMS DALI ZANGURASHVILI
"... Abstract. The paper develops the previously proposed approach to constructing factorization systems in general categories. This approach is applied to the problem of finding conditions under which a functor (not necessarily admitting a right adjoint) “reflects” factorization systems. In particular, ..."
Abstract
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Abstract. The paper develops the previously proposed approach to constructing factorization systems in general categories. This approach is applied to the problem of finding conditions under which a functor (not necessarily admitting a right adjoint) “reflects” factorization systems. In particular, a generalization of the wellknown CassidyHébertKelly factorization theorem is given. The problem of relating a factorization system to a pointed endofunctor is considered. Some relevant examples in concrete categories are