Some Results on Locally Finitely Presentable Categories

DOI10.2307/2000508zbMath0615.18002OpenAlexW4256129919MaRDI QIDQ4723928

Andrew M. Pitts, Michael Makkai

Publication date: 1987

Full work available at URL: https://doi.org/10.2307/2000508

zbMATH Keywords

structurelocally finitely presentable categoriesglobal sections of sheafsmall categories with finite limits

Mathematics Subject Classification ID

Categorical logic, topoi (03G30) Special categories (18B99) Theories (e.g., algebraic theories), structure, and semantics (18C10) Categories admitting limits (complete categories), functors preserving limits, completions (18A35)

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Gabriel-Ulmer duality for topoi and its relation with site presentations ⋮ The HASCASL prologue: Categorical syntax and semantics of the partial \(\lambda\)-calculus ⋮ General facts on the Scott adjunction ⋮ Descent and duality ⋮ Unnamed Item ⋮ Accessibility and presentability in 2-categories ⋮ Elementary categories ⋮ A theorem on Barr-exact categories, with an infinitary generalization ⋮ Enriched Locally Generated Categories ⋮ Syntactic characterizations of closure under pullbacks and of locally polypresentable categories ⋮ Amalgamation in the semantics of CASL ⋮ On the fullness of certain functors ⋮ Algebraic theories of quasivarieties ⋮ Classifying categories for partial equational logic ⋮ Quasi-coproducts and accessible categories with wide pullbacks ⋮ A simple characterization of theories of varieties ⋮ Unnamed Item

Cites Work

• First order categorical logic. Model-theoretical methods in the theory of topoi and related categories
• Preservation theorems for limits of structures and global sections of sheaves of structures
• Model theory
• Lokal präsentierbare Kategorien. (Locally presentable categories)
• Seminar of algebraic geometry du Bois-Marie 1963--1964. Topos theory and étale cohomology of schemes (SGA 4). Vol. 1: Topos theory. Exp. I--IV
• Sheaves of structures and generalized ultraproducts
• Introduction to bicategories
• INJECTIVITY IN CATEGORIES TO REPRESENT ALL FIRST ORDER FORMULAS, I
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