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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 systems. In particular, ..."
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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
Comment.Math.Univ.Carolinae 41,1 (2000)9{24 9 Totality of product completions
"... Abstract. Categories whose Yoneda embedding has a left adjoint are known as total categories and are characterized by a strong cocompleteness property. Weintroduce the notion of multitotal category A by asking the Yoneda embedding A![A op; Set] tobe right multiadjoint and prove that this property is ..."
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Abstract. Categories whose Yoneda embedding has a left adjoint are known as total categories and are characterized by a strong cocompleteness property. Weintroduce the notion of multitotal category A by asking the Yoneda embedding A![A op; Set] tobe right multiadjoint and prove that this property is equivalent to totality of the formal product completion A of A. We also characterize multitotal categories with various types of generators; in particular, the existence of dense generators is inherited by the formal product completion i measurable cardinals cannot be arbitrarily large.
Totality of Product Completions
"... Categories whose Yoneda embedding has a left adjoint are known as ..."
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