Fiore, T. M. Pseudo algebras and pseudo double categories. (English) Zbl 1184.18003 J. Homotopy Relat. Struct. 2, No. 2, 119-170 (2007). Summary: As an example of the categorical apparatus of pseudo algebras over 2-theories, we show that pseudo algebras over the 2-theory of categories can be viewed as pseudo double categories with folding or as appropriate 2-functors into bicategories. Foldings are equivalent to connection pairs, and also to thin structures if the vertical and horizontal morphisms coincide. In a sense, the squares of a double category with folding are determined in a functorial way by the 2-cells of the horizontal 2-category. As a special case, strict 2-algebras with one object and everything invertible are crossed modules under a group. Cited in 10 Documents MSC: 18D05 Double categories, \(2\)-categories, bicategories and generalizations (MSC2010) 18C10 Theories (e.g., algebraic theories), structure, and semantics 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics Keywords:2-algebra; 2-category; 2-group; 2-theory; algebra; bicategory; coherence; connection pair; crossed module; double category; double group; folding; holonomy; pseudo algebra; pseudo double category; thin structure PDFBibTeX XMLCite \textit{T. M. Fiore}, J. Homotopy Relat. Struct. 2, No. 2, 119--170 (2007; Zbl 1184.18003) Full Text: arXiv EuDML EMIS