Locally Presentable and Accessible CategoriesThe concepts of a locally presentable category and an accessible category are extremely useful in formulating connections between universal algebra, model theory, logic, and computer science. The aim of this book is to provide an exposition of both the theory and the applications of these categories at a level accessible to graduate students. The concepts of lambda-presentable objects, locally lambda-presentable categories, and lambda-accessible categories are discussed in detail. The authors prove that Freyd's essentially algebraic categories are precisely the locally presentable categories. In the final chapter, they treat some advanced topics in model theory. |
Contents
0 Preliminaries | 1 |
1 Locally Presentable Categories | 7 |
2 Accessible Categories | 67 |
3 Algebraic Categories | 131 |
4 Injectivity Classes | 173 |
5 Categories of Models | 199 |
6 Vopěnkas Principle | 241 |
Large Cardinals | 281 |
Open Problems | 295 |
Bibliography | 299 |
| 309 | |
| 313 | |
Common terms and phrases
A-accessible A-presentable objects A-pure A-small Abelian groups accessible category accessible functor accessibly embedded Adámek adjoint analogous arity Assuming Vopěnka's principle axiomatizable binary relation canonical diagram category of models closed under A-directed closed under products cocomplete coequalizer cofinal colim comma-category compatible cocone cone cone-reflective Corollary defined denote dense subcategory directed diagram Dobj E-structures epimorphism equations equivalent Example fact factorizes finitary finitely accessible finitely presentable finitely presentable category follows forgetful functor formula full embedding full subcategory functor F given graphs hom-functors homomorphism implies isomorphism locally finitely presentable locally presentable category many-sorted maps monomorphisms morphism f ordinal orthogonality class phism poset Pres preserves A-directed colimits PROOF Proposition prove quasivariety quotient reflective subcategory regular cardinal Remark Rosický S-sorted sentable signature small category split idempotents split subobjects subcategory of Set subobjects subset Theorem variables Vopěnka's principle