Abstract elementary classes and accessible categories

  title={Abstract elementary classes and accessible categories},
  author={Tibor Beke and Jir{\'i} Rosick{\'y}},
  journal={Ann. Pure Appl. Log.},
Approximations of superstability in concrete accessible categories
We generalize the constructions and results of Chapter 10 in Baldwin's "Categoricity" to coherent accessible categories with concrete directed colimits and concrete monomorphisms. In particular, we
Limits of abstract elementary classes
We show that the category of abstract elementary classes (AECs) and concrete functors is closed under constructions of "limit type," which generalizes the approach of Mariano, Zambrano and Villaveces
Universal abstract elementary classes and locally multipresentable categories
We exhibit an equivalence between the model-theoretic framework of universal classes and the category-theoretic framework of locally multipresentable categories. We similarly give an equivalence
A generalization of a recent result of Boney on tameness under a large cardinal assumption is proved, which shows that a number of results on abstract elementary classes (AECs) hold in accessible categories with concrete directed colimits.
Abstract We show that metric abstract elementary classes (mAECs) are, in the sense of [15], coherent accessible categories with directed colimits, with concrete ℵ1-directed colimits and concrete
Sizes and filtrations in accessible categories
Accessible categories admit a purely category-theoretic replacement for cardinality: the internal size. Generalizing results and methods from [LRV19b], we examine set-theoretic problems related to
Combinatorial Homotopy Categories
A model category is called combinatorial if it is cofibrantly generated and its underlying category is locally presentable. As shown in recent years, homotopy categories of combinatorial model
Large Cardinal Axioms from Tameness in AECs
We show that various tameness assertions about abstract elementary classes imply the existence of large cardinals under mild cardinal arithmetic assumptions.
Bootstrapping structural properties, via accessible images
We present several new model-theoretic applications of the fact that, under a mild large cardinal assumption, the powerful image of any accessible functor is accessible. In particular, we generalize


Category-theoretic aspects of abstract elementary classes
More on directed colimits of models
This work generalizes M. Richter's result to classes of ∑-structures having an infinitary first-order axiomatization in a larger signature ∑′ and shows that, as categories, these classes have a natural characterization.
Abstract elementary classes and infinitary logics
  • D. Kueker
  • Mathematics
    Ann. Pure Appl. Log.
  • 2008
Topological and category-theoretic aspects of abstract elementary classes
ly, any split monomorphism is λ-pure. The converse, while true in Set, does not hold in general. A necessary and sufficient condition for λ-purity can be given provided we are working in a category
Accessible Categories, Saturation and Categoricity
Model theoretic concepts of saturation and categoricity are studied in the context of accessible categories to explore the role of categories in the development of knowledge.
Some Obstacles to Duality in Topological Algebra
0. Introduction. Functors form an equivalence of categories (see [8,]) if Γ(Φ(A)) ≅ A and Φ (Γ(B)) ≅ B naturally for all objects A from and B from . Letting denote the opposite of we say that and are
Accessible categories : the foundations of categorical model theory
[F-S] D. Fremlin and S. Shelah, Pointwise compact and stable sets of measurable functions, manuscript, 1990. [G-G-M-S] N. Ghoussoub, G. Godefroy, B. Maurey, W. Schachermayer, Some topological and
More on Compact Hausdorff Spaces and Finitary Duality
It is an old conjecture by P. Bankston that the category CompHaus of compact Hausdorff spaces and their continuous maps is not dually equivalent to any elementary P-class of finitary algebras (taken
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
Math. Soc
  • Math. Soc
  • 2009