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MCompleteness Is Seldom Monadic Over Graphs
 THEORY APPL. CATEG
, 2000
"... For a set M of graphs the category CatM of all Mcomplete categories and all strictly Mcontinuous functors is known to be monadic over Cat. The question of monadicity of CatM over the category of graphs is known to have an affirmative answer when M specifies either (i) all finite limits, or (ii ..."
Abstract

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For a set M of graphs the category CatM of all Mcomplete categories and all strictly Mcontinuous functors is known to be monadic over Cat. The question of monadicity of CatM over the category of graphs is known to have an affirmative answer when M specifies either (i) all finite limits, or (ii) all finite products, or (iii) equalizers and terminal objects, or (iv) just terminal objects. We prove that, conversely, these four cases are (essentially) the only cases of monadicity of CatM over the category of graphs, provided that M is a set of finite graphs containing the empty graph.
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 ..."
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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: