Laplaza Sets, or How to Select Coherence Diagrams for Pseudo Algebras

Abstract

We define a general concept of pseudo algebras over theories and 2-theories. A more restrictive such notion was introduced by Hu and Kriz, but as noticed by M. Gould, did not capture the desired examples. The approach taken in this paper corrects the mistake by introducing a more general concept, allowing more flexibility in selecting coherence diagrams for pseudo algebras.Comment: 21 pages. To appear in the Advances of Mathematics. Exposition improved, notion of operad with degeneracies removed as a simplification, definition of pseudo algebra improved