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, 2000

"... 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 unificat ..."

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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:

### Scetches and Specifications . . .

, 2000

"... 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 unificat ..."

Abstract
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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:

### Mosaics for Specifications with Implicit State

, 2000

"... In this paper, we develop a new framework for algebraicspecifications with implicit state. Among other results, this bridges the gap between specifications with implicit state and with explicit state. ..."

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In this paper, we develop a new framework for algebraicspecifications with implicit state. Among other results, this bridges the gap between specifications with implicit state and with explicit state.

### Scetches and Specifications User'S Gude -- First . . .

, 2000

"... 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 unificat ..."

Abstract
- Add to MetaCart

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:

### Remarks on 2-Groups

, 2008

"... A 2-group is a ‘categorified ’ version of a group, in which the underlying set G has been replaced by a category and the multiplication map m:G× G → G has been replaced by a functor. A number of precise definitions of this notion have already been explored, but a full treatment of their relationship ..."

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A 2-group is a ‘categorified ’ version of a group, in which the underlying set G has been replaced by a category and the multiplication map m:G× G → G has been replaced by a functor. A number of precise definitions of this notion have already been explored, but a full treatment of their relationships is difficult to extract from the literature. Here we describe the relation between two of the most important versions of this notion, which we call ‘weak ’ and ‘coherent ’ 2-groups. A weak 2-group is a weak monoidal category in which every morphism has an inverse and every object x has a ‘weak inverse’: an object y such that x ⊗ y ∼ = 1 ∼ = y ⊗ x. A coherent 2-group is a weak 2-group in which every object x is equipped with a specified weak inverse ¯x and isomorphisms ix:1 → x⊗¯x, ex: ¯x⊗x → 1 forming an adjunction. We define 2-categories of weak and coherent 2-groups and construct an ‘improvement ’ 2-functor which turns weak 2-groups into coherent ones; using this one can show that these 2-categories are biequivalent. We also internalize the concept of a coherent 2-group. This gives a way of defining topological 2-groups, Lie 2-groups, and the like. 1