Algebra, Logic and Topology

 

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Title
Paracategories and Saturated Partial Algebras

Abstract
Freyd´s notion of paracategory embodies a system of morphisms subject to partial compositions. We give an abstract axiomatisation of this notion internally in a regular category admitting free monoids. This leads us to consider the more general notion of partial algebras relative to a monad. We introduce for these the crucial notion of saturation (which is characteristic of paracategories) in order to characterise their representability. We explore also the 2-dimensional aspects of the theory of paracategories, most notably the notion of adjunction, in order to capture Freyd´s proposed example of the cartesian closed paracategory of dinatural transformations. References: Paracategories I: Internal Paracategories and Saturated Partial Algebras by C. Hermida and P. Mateus (Theoretical Computer Science, 309, 125-156 2003). Paracategories II: Adjunctions, fibrations and examples from probabilistic automata theory by C. Hermida and P. Mateus (Theoretical Computer Science, 311, 71-103 2004).

Areas of interest
Category Theory

Speaker(s)
Claudio Hermida (Instituto Superior Técnico, Lisboa)

Date
November 12, 2004

Time
15.00

Room
5.5

 
     
 

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