Algebraic exponentiation in general categories

DOI10.1007/s10485-011-9251-6zbMath1276.18002OpenAlexW2035538171MaRDI QIDQ1928245

James Richard Andrew Gray

Publication date: 2 January 2013

Published in: Applied Categorical Structures (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10485-011-9251-6

zbMATH Keywords

protomodular categoryadjoint functorsemi-abelian categorysplit extensioninternal actionpullback functoralgebraic exponentiation(weakly) Mal'tsev category(weakly) unital category

Mathematics Subject Classification ID

Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) (18A40) Special properties of functors (faithful, full, etc.) (18A22) Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) (18A30) Categories admitting limits (complete categories), functors preserving limits, completions (18A35) Closed categories (closed monoidal and Cartesian closed categories, etc.) (18D15) Accessible and locally presentable categories (18C35) Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads (18C15) Definitions and generalizations in theory of categories (18A05) Functor categories, comma categories (18A25) Eilenberg-Moore and Kleisli constructions for monads (18C20)

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Cites Work

• Algebraic exponentiation in general categories
• On exponentiability of étale algebraic homomorphisms
• Obstruction theory in algebraic categories. I
• COMMUTATOR, NILPOTENCY, AND SOLVABILITY IN CATEGORIES
• Upper Central Series in a Category.
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