Combinatorial Functors

0. Introduction.- I. Categories and Functors.- 1. Categories.- 2. Morphism Combinatorial Functors.- 3. Combinatorial Functors.- II. Model Theory.- 4. Countable Atomic Models.- 5. Copying.- 6. Dimension.- III. Combinatorial Functions.- 7. Strict Combinatorial Functors.- 8. Strict Combinatorial Functions.- IV. Recursive Equivalence.- 9. Suitable Categories.- 10. Bridge.- 11. Recursive Equivalence (Sets).- 12. Recursive Equivalence (Linear Orderings).- 13. Recursive Equivalence in a General Setting.- 14. Existence of Dedekind Types.- 15. Partial Recursive Combinatorial Functors.- 16. Partial Recursive Strict Combinatorial Functors.- V. Identities.- 17. The Strong Topology.- 18. Extending Identities to Dedekind Dense Types.- 19. More on Identities.- 20. Uniform Implications for Dedekind Types.- VI. Frames.- 21. Frames.- 22. Frame Maps are Map Frames.- 23. Recursive Frame Maps are Recursive Map Frames.- 24. Chains and Chain Types.- 25. Extending Relations Using Frames.- VII. The Dimension Case.- 26. Extensions of Solutions of Equations.- 27. Universal Horn Sentences.- 28. Universal Sentences I.- 29. Universal Sentences II.- VIII. Sound Values.- 30. Soundly Based Types.- 31. Extending Partial Functions to Soundly Based Types.- 32. Functions from Infinite Dedekind Types to Soundly Based Dedekind Types.- 33. Total Functions to Soundly Based Dedekind Types.- IX. The Automorphism Extension Property.- 34. The Automorphism Extension Property.- 35. Regressive Types and Tree Frames.- 36. Solutions of Equations and the Automorphism Extension Property.- X. Satisfiability.- 37. Finitary Relations.- 38. The Master Frame.- 39. Satisfiability.- 40. Compactness and Dimension.- Index of Notations.- General Index.