Equivalens in Proofs of Categorial Proof Theory

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Equivalens in Proofs of Categorial Proof Theory

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dc.contributor.advisor Došen, Kosta
dc.contributor.author Petrić, Zoran en_US
dc.date.accessioned 2009-12-03T12:14:12Z
dc.date.available 2009-12-03T12:14:12Z
dc.identifier.uri http://hdl.handle.net/123456789/187
dc.description.abstract In this dissertation methods of the proof theory are used to investigate coherence in some categories. Moreover, it is shown what the categorical notion of coherence means in the categorial proof theory. The thesis consists of three chapters. MacLane’s results for monoidal categories and symmetric monoidal categories are extended in Chapter 1 of the dissertation to some other categories with multiplication: relevant categories, affine categories and symmetric monoidal categories. All the results are formulated in terms of natural transformations equipped with “grafs” (g-natural transformations). It is proved, as consequences of these results, that relevant categories, affine categories and symmetric monoidal categories have the coherence property. Moreover, using these results, some basic relations between the free categories of these classes of categories are presented in Chapter 2 of the dissertation. In Chapter 3, an extension of the notion of dinatural transfomation is introduced in order to give a criterion of preservation of dinaturality under composition. An example of an application is given by proving that all cartesian closed canonical categories transformations are dinatural. Finally, an alternative sequent system for a fragment of intuitionistic propositional logic is introduced as a device, and a cut-elimination procedure is established for this system.
dc.description.provenance Made available in DSpace on 2009-12-03T12:14:12Z (GMT). No. of bitstreams: 1 phdZoranPetric.pdf: 3130667 bytes, checksum: c85b7f5390eddaee19b4a942a724d305 (MD5) en
dc.publisher Belgrade en_US
dc.title Equivalens in Proofs of Categorial Proof Theory en_US
dc.title.alternative Jednakosti izvođenja u kategorijalnoj teoriji dokaza sr
mf.subject.keywords supstrictural logics, symmetric monoidal categories, cartesian categories, coherence, dinatural transformations, cartesian closed categories
mf.contributor.committee Vujošević, Slobodan; Božić, Milan; Lipkovski, Aleksandar

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