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Pseudo algebras and pseudo double categories
 J. Homotopy Relat. Struct
"... Abstract. As an example of the categorical apparatus of pseudo algebras over 2theories, we show that pseudo algebras over the 2theory of categories can be viewed as pseudo double categories with folding or as appropriate 2functors into bicategories. Foldings are equivalent to connection pairs, an ..."
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Abstract. As an example of the categorical apparatus of pseudo algebras over 2theories, we show that pseudo algebras over the 2theory of categories can be viewed as pseudo double categories with folding or as appropriate 2functors 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 2cells of the horizontal 2category. As a special case, strict 2algebras with one object and everything invertible are crossed modules under a group.
unknown title
, 806
"... Sur l’existence d’une catégorie ayant une matrice strictement positive donnée ..."
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Sur l’existence d’une catégorie ayant une matrice strictement positive donnée
Journal of Homotopy and Related Structures, vol. 2(2), 2007, pp.119–170 PSEUDO ALGEBRAS AND PSEUDO DOUBLE CATEGORIES
"... As an example of the categorical apparatus of pseudo algebras over 2theories, we show that pseudo algebras over the 2theory of categories can be viewed as pseudo double categories with folding or as appropriate 2functors into bicategories. Foldings are equivalent to connection pairs, and also to ..."
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As an example of the categorical apparatus of pseudo algebras over 2theories, we show that pseudo algebras over the 2theory of categories can be viewed as pseudo double categories with folding or as appropriate 2functors 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 2cells of the horizontal 2category. As a special case, strict 2algebras with one object and everything invertible are crossed modules under a group. 1.
STRICT 2GROUPS ARE CROSSED MODULES SVENS. PORST
, 812
"... ABSTRACT. The 2categories of strict 2groups and crossed modules are introduced and their 2equivalence is made explicit. ..."
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ABSTRACT. The 2categories of strict 2groups and crossed modules are introduced and their 2equivalence is made explicit.
DAMTP200327 Higher Gauge Theory and a nonAbelian generalization
, 2003
"... In conventional gauge theory, a charged point particle is described by a representation of the gauge group. If we propagate the particle along some path, the parallel transport of the gauge connection acts on this representation. The Lagrangian density of the gauge field depends on the curvature of ..."
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In conventional gauge theory, a charged point particle is described by a representation of the gauge group. If we propagate the particle along some path, the parallel transport of the gauge connection acts on this representation. The Lagrangian density of the gauge field depends on the curvature of the connection which can be calculated from the holonomy around (infinitesimal) loops. For Abelian symmetry groups, say G = U(1), there exists a generalization, known as pform electrodynamics, in which (p − 1)dimensional charged objects can be propagated along psurfaces and in which the Lagrangian depends on a generalized curvature associated with (infinitesimal) closed psurfaces. In this article, we use Lie 2groups and ideas from higher category theory in order to formulate a discrete gauge theory which generalizes these models at the level p = 2 to possibly nonAbelian symmetry groups. The main new feature is that our model involves both parallel transports along paths and generalized transports along surfaces with a nontrivial interplay of these two types of variables. We construct the precise assignment of variables to the curves and surfaces, the generalized local symmetries and gauge invariant actions and we clarify which structures can be nonAbelian and which others are always Abelian. A discrete version of connections on nonAbelian gerbes is a special case of our construction. Even though the motivation sketched so far suggests applications mainly in string theory, the model presented here is also related to spin foam models of quantum gravity and may in addition provide some insight into the role of centre monopoles and vortices in lattice QCD.