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algebra universalis

, Volume 39, Issue 3–4, pp 121–144 | Cite as

Representability and local representability of algebraic theories

  • V. Trnková

Abstract.

A finitary monosorted algebraic theory \( \cal T \) is called locally representable (or representable) in a category \( \cal K \) with finite products if every its initial segment is the domain of a full faithful finite-products-preserving functor into \( \cal K \) (or if \( \cal T \) itself is the domain of such a functor). The question of when local representability implies representability is discussed, and theories \( \cal T \) for which local representability always implies representability are fully characterized.

Key words and phrases: Algebraic theory, abstract clone, segments, finite-products-preserving full embeddings. 

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Copyright information

© Birkhäuser Verlag Basel, 1998

Authors and Affiliations

  • V. Trnková
    • 1
  1. 1.Mathematics Institute, Charles University, Sokolovska 83, CZ-18675 Praha, Czech Republic. E-mail: trnkova@karlin.mff.cuni.czCZ

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