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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 ..."
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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.
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, 2006
"... Two distinct pools of Src family tyrosine kinases regulate PDGFinduced DNA synthesis and actin dorsal ruffles ..."
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Two distinct pools of Src family tyrosine kinases regulate PDGFinduced DNA synthesis and actin dorsal ruffles
Preprint Number 15–09 LAX ORTHOGONAL FACTORISATION SYSTEMS
"... Abstract: This paper introduces lax orthogonal algebraic weak factorisation systems on 2categories and describes a method of constructing them. The related notions of KZ lifting operation, lax natural lifting operation and lax orthogonality between morphisms are studied, and a number of examples p ..."
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Abstract: This paper introduces lax orthogonal algebraic weak factorisation systems on 2categories and describes a method of constructing them. The related notions of KZ lifting operation, lax natural lifting operation and lax orthogonality between morphisms are studied, and a number of examples provided. These examples rest in the notion of simple 2monad, that is a generalisation of the simple reflections studied by Cassidy, Hébert and Kelly. Each simple 2monad on a finitely complete 2category gives rise to a lax orthogonal algebraic weak factorisation system. Examples of simple 2monads are: completion under a class of colimits, the filter monad on topological spaces and Cauchy completion on Lawvere’s metric spaces.
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, 2006
"... Hardy and BMO spaces associated to divergence form elliptic operators ..."
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