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Keywords:
initial morphism; (extremal) monomorphism; faithful functor; semicategory
initial morphism; (extremal) monomorphism; faithful functor; semicategory
Summary:
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 additional conditions) a morphism is initial w.r.t. all faithful functors that map extremal monomorphisms to monomorphisms iff it is an extremal monomorphism.
References:
[1] Adámek J., Herrlich H., Strecker G.E.: Abstract and Concrete Categories. Wiley Interscience New York (1990). MR 1051419
[2] Bénabou J.: Fibered categories and the foundations of category theory. J. Symb. Logic 50 (1985), 10-37. MR 0780520
[3] Borceux F.: Handbook of Categorical Algebra 2. Cambridge University Press (1994). MR 1313497 | Zbl 0843.18001
[4] Grothendieck A.: Catégories fibrées et descente. Revêtements étales et groupe fondamental, Séminaire de Géometrie Algébrique du Bois-Marie 1960/61 (SGA 1), Exposé VI, 3rd ed. Institut des Hautes Etudes Scientifiques Paris 1963 reprint Springer Lect. Notes Math. 224 1971 145-194. MR 0354651
[5] Herrlich H., Strecker G.E.: Category Theory. 2nd ed. Heldermann Berlin (1979). MR 0571016 | Zbl 0437.18001
[6] Hong S.S.: Categories in which every monosource is initial. Kyungpook Math. J. 15 (1975), 133-139. MR 0369466
[7] Klop J.W.: Term rewriting systems. Handbook of Logic in Computer Science, vol. 2 (S. Abramsky, D.M. Gabbay, and T.S.E. Maibaum, eds.), Oxford University Press, 1992, pp.1-116. MR 1381696 | Zbl 1030.68053
[8] Schröder L.: Composition graphs and free extensions of categories. German PhD Thesis, University of Bremen Logos Verlag Berlin (1999).
[9] Schröder L.: Traces of epimorphism classes. J. Pure Appl. Algebra, submitted.
[10] Schröder L., Herrlich H.: Free adjunction of morphisms. Appl. Cat. Struct., to appear. MR 1799731
[11] Schröder L., Herrlich H.: Free factorizations. Appl. Cat. Struct., to appear. MR 1866871
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