Locally Presentable and Accessible Categories is a book by Jiří Adámek and Jiří Rosický about, unsurprisingly, locally presentable and accessible categories. It was published by Cambridge University Press in the London Mathematical Society Lecture Note Series, number 189, in 1994.
accessible categories: see also sketch
algebraic categories: see algebraic category, equationally presentable category, essentially algebraic theory, and variety of algebras
injectivity class?es: see also weak factorization system
categories of models: see internal logic, theory, essentially algebraic theory, model
Locally presentable categories: Cocomplete possibly-large categories generated under filtered colimits by small generators under small relations. Equivalently, accessible localizations of free cocompletions. Accessible categories omit the cocompleteness requirement; toposes add the requirement of a left exact localization.
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