Allegories of Passing in Bill T. Jones

Groups in Allegories

Groups are one of the most fundamental notions in mathematics. This paper provides a foundation of group theory in allegories. Almost all results in the paper can be applied to theory of fuzzy groups.

Complements in Distributive Allegories

It is know in topos theory that axiom of choice implies that the topos is Boolean. In this paper we want to prove and generalize this result in the context of allegories. In particular, we will show that partial identities do have complements in distributive allegories with relational sums and total splittings assuming the axiom of choice. Furthermore, we will discuss possible modifications of ...

Cardinality in Allegories

In this paper we want to investigate two notions of the cardinality of relations in the context of allegories. The different axiom systems are motivated on the existence of injective and surjective functions, respectively. In both cases we provide a canonical cardinality function and show that it is initial in the category of all cardinality functions over the given allegory.

T. Duckett Jones and rheumatic fever in 1986. T. Duckett Jones Memorial Lecture.

Allegories of Circuits

This paper presents three paradigms for circuit design, and investigates the relationships between them. These paradigms are syntactic (based on Freyd and Scedrov's unitary pre-tabular allegories (upas)), pictorial (based on the net list model of circuit connectivity), and relational (based on Sheeran's relational model of circuit design Ruby). We show that net lists over a given signature cons...