category-theory

There are several contexts in which it is of relevance that a certain property of a morphism is preserved (or stable) under pullback, i.e. also shared by the the morphism for any pullback diagram Geometers prefer to say “stable under base change”. Monomorphisms are always stable under pullback; that is, if is a monomorphism, then so is . Epimorphisms are not necessarily stable under pullback. In …

John Martin Elliott Hyland is Professor in Mathematical Logic in the University of Cambridge, and is a Fellow of King’s College, Cambridge. Hyland is known for work on the effective topos (within topos theory), on the lambda-calculus and on game semantics. His main research interests are in the following: Mathematical Logic: Lambda Calculus, Recursion Theory, Realizability, Proof Theory, Linear L…

A small presheaf on a category is a presheaf which is determined by a small amount of data. If is itself small, then every presheaf on is small, but this is no longer true when is large. In many cases, when is large, it is the small presheaves which seem to be more important and useful. Let be a category which is locally small, but possibly large. A presheaf is small if it is the left Kan extensi…