An introduction to stack-algebras

Abstract

In this thesis, I have introduced the concept of a stack-algebra, and explored some of the fundamental properties associated with this. Many of the ideas originated from the class notes, "Sheaves and Logic," by Dana Scott, (unpublished), Oxford 1974, in which he developed the notion of a 'stack over a topological space,' and compared this structure with that of a sheaf over a topological space. The axiomatic concept of a 'stack over a complete Heyting algebra' is also due to Scott and gives the study of stacks a more abstract flavor. Thus the concept of a stack-algebra arises from that of a stack, by placing on the stack a collection of finitary operations which blend in a natural way with those stack operations already present.