The papers in this volume were presented at the fourthbiennial Summer Conference on Category Theory and ComputerScience, held in Paris, September3-6, 1991. Category theorycontinues to be an important tool in foundationalstudies incomputer science. It has been widely applied by logicians toget concise interpretations of many logical concepts. Linksbetween logic and computer science have been developed nowfor over twenty years, notably via the Curry-Howardisomorphism which identifies programs with proofs and typeswith propositions. The triangle category theory - logic -programming presents a rich world of interconnections. Topics covered in this volume include the following. Typetheory: stratification of types and propositions can bediscussed in a categorical setting. Domain theory: syntheticdomain theory develops domain theory internally in theconstructive universe of the effective topos. Linear logic:the reconstruction of logic based on propositions asresources leads to alternatives to traditional syntaxes. Theproceedings of the previous three category theoryconferences appear as Lecture Notes in Computer ScienceVolumes 240, 283 and 389.