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Title: Dualities and finitely presented functors
Author: Dean, Samuel
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2017
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We investigate various relationships between categories of functors. The major examples are given by extending some duality to a larger structure, such as an adjunction or a recollement of abelian categories. We prove a theorem which provides a method of constructing recollements which uses 0-th derived functors. We will show that the hypotheses of this theorem are very commonly satisfied by giving many examples. In our most important example we show that the well-known Auslander-Gruson-Jensen equivalence extends to a recollement. We show that two recollements, both arising from different characterisations of purity, are strongly related to each other via a commutative diagram. This provides a structural explanation for the equivalence between two functorial characterisations of purity for modules. We show that the Auslander-Reiten formulas are a consequence of this commutative diagram. We define and characterise the contravariant functors which arise from a pp-pair. When working over an artin algebra, this provides a contravariant analogue of the well-known relationship between pp-pairs and covariant functors. We show that some of these results can be generalised to studying contravariant functors on locally finitely presented categories whose category of finitely presented objects is a dualising variety.
Supervisor: Prest, Michael Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Additive category ; Abelian category ; Hilton-Rees embedding ; Contravariant functor ; pp-pair ; Localisation ; Auslander-Gruson-Jensen duality ; Auslander-Reiten formulas ; Finitely presented functor ; Locally finitely presented category ; Recollement of abelian categories