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Abstract initiality

Lutz Schröder, Horst Herrlich (2000)

Commentationes Mathematicae Universitatis Carolinae

We study morphisms that are initial w.r.t. all functors in a given conglomerate. Several results and counterexamples are obtained concerning the relation of such properties to different notions of subobject. E.g., strong monomorphisms are initial w.r.t. all faithful adjoint functors, but not necessarily w.r.t. all faithful monomorphism-preserving functors; morphisms that are initial w.r.t. all faithful monomorphism-preserving functors are monomorphisms, but need not be extremal; and (under weak...

Bimorphisms in pro-homotopy and proper homotopy

Jerzy Dydak, Francisco Ruiz del Portal (1999)

Fundamenta Mathematicae

A morphism of a category which is simultaneously an epimorphism and a monomorphism is called a bimorphism. The category is balanced if every bimorphism is an isomorphism. In the paper properties of bimorphisms of several categories are discussed (pro-homotopy, shape, proper homotopy) and the question of those categories being balanced is raised. Our most interesting result is that a bimorphism f:X → Y of t o w ( H 0 ) is an isomorphism if Y is movable. Recall that ( H 0 ) is the full subcategory of p r o - H 0 consisting of...

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