On completeness and cocompleteness in and around small categories

DOI10.1016/0168-0072(94)00035-2zbMath0829.18001OpenAlexW1966573209MaRDI QIDQ1896485

Dusko Pavlovic

Publication date: 17 January 1996

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-0072(94)00035-2

zbMATH Keywords

small categoriestoposesaccessible categoriescartesian closedadjoint functor theoremequivalence of completeness and cocompleteness

Mathematics Subject Classification ID

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Categorical logic, topoi (03G30) Topoi (18B25) Fibered categories (18D30) Categories admitting limits (complete categories), functors preserving limits, completions (18A35) Other constructive mathematics (03F65)

Related Items (3)

Maps. I: Relative to a factorisation system ⋮ Logical systems. I: Internal calculi. ⋮ Programs, Grammars and Arguments: A Personal View of some Connections between Computation, Language and Logic

Uses Software

• Automath

Cites Work

• The calculus of constructions
• A small complete category
• Categories of continuous functors. I
• ABOUT MODEST SETS
• The Discrete Objects in the Effective Topos
• Fibered categories and the foundations of naive category theory
• Constructive natural deduction and its ‘ω-set’ interpretation
• Adjointness in Foundations
• Colimits in Topoi
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