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Ordered categories with involution

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CONTENTS Introduction..........................................................................................................................................................................5 §1. Categories with involution, ordered categories and ordered categories with involution.................................................8 §2. Types of morphisms regularity in an OI-category. Functional and difunctional morphisms...........................................17 §3. Equivalences and coequivalences. Congruences and cocongruences........................................................................25 §4. Modular categories and correspondence categories...................................................................................................31 §5. A construction of correspondence categories. Admissible and exact functors.............................................................40 §6. Correspondences over sites........................................................................................................................................52 §7. Modular categories with images...................................................................................................................................58 §8. Correspondence categories over categories of classes R₁-R₃....................................................................................62 §9. Correspondence categories over exact categories......................................................................................................69 §10. OI-categories with a quasinull object..........................................................................................................................75 §11. Correspondence categories over exact categories with a null object, over additive and abelian categories..............83 §12. Quaternar categories.................................................................................................................................................88 §13. Construction of quaternar categories.........................................................................................................................93 §14. Supplementary notes and questions........................................................................................................................105 References.......................................................................................................................................................................110
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