Factorizations in bicategories Many factorization structures which are known in Cat and in other bicategories are of a "regular" type, in the sense that they can be obtained by universal (weighted) constructions. For an arrow in a bicategory, the kernel is defined by suitable weighted limits while a colimit construction relative to the same weights gives the corresponding notion of quotient. The main result consists in the fact that the process of taking kernels is right bi-adjoint to that of taking quotients. The counit of this bi-adjunction provides 1 a canonical factorization of any arrow. We give suitable conditions, both on weights and on bicategories, in order that this canonical construction provide a factorization structure. This is joint work with D. Schumacher. BISSON, T. Covering Spaces as Operations in Cobordism Theory For any finite covering space over a closed manifold we define an operation in the category of manifolds and study t

SKETCHES AND SPECIFICATIONS is a common denomination for several papers which deal with applications of Ehresmann’s sketch theory to computer science. These papers can be considered as the first steps towards a unified theory for software engineering. However, their aim is not to advocate a unification of computer languages; they are designed to build a frame for the study of notions which arise from several areas in computer science. These papers are arranged in two complementary families: REFERENCE MANUAL and USER’S GUIDE. The reference manual provides general definitions and results, with comprehensive proofs. On the other hand, the user’s guide places emphasis on motivations and gives a detailed description of several examples. These two families, though complementary, can be read independently. No prerequisite is assumed; however, it can prove helpful to be familiar either with specification techniques in computer science or with category theory in mathematics. These papers are under development, they are, or will be, available at:

SKETCHES AND SPECIFICATIONS is a common denomination for several papers which deal with applications of Ehresmann’s sketch theory to computer science. These papers can be considered as the first steps towards a unified theory for software engineering. However, their aim is not to advocate a unification of computer languages; they are designed to build a frame for the study of notions which arise from several areas in computer science. These papers are arranged in two complementary families: REFERENCE MANUAL and USER’S GUIDE. The reference manual provides general definitions and results, with comprehensive proofs. On the other hand, the user’s guide places emphasis on motivations and gives a detailed description of several examples. These two families, though complementary, can be read independently. No prerequisite is assumed; however, it can prove helpful to be familiar either with specification techniques in computer science or with category theory in mathematics. These papers are under development, they are, or will be, available at: