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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.
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.
WHAT IS THE JACOBIAN OF A RIEMANN SURFACE WITH BOUNDARY?
, 2008
"... Abstract. We define the Jacobian of a Riemann surface with analytically parametrized boundary components. These Jacobians belong to a moduli space of “open abelian varieties ” which satisfies gluing axioms similar to those of Riemann surfaces, and therefore allows a notion of “conformal field theory ..."
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Abstract. We define the Jacobian of a Riemann surface with analytically parametrized boundary components. These Jacobians belong to a moduli space of “open abelian varieties ” which satisfies gluing axioms similar to those of Riemann surfaces, and therefore allows a notion of “conformal field theory ” to be defined on this space. We further prove that chiral conformal field theories corresponding to even lattices factor through this moduli space of open abelian varieties. 1.
A MATHEMATICAL FORMALISM FOR THE KONDO EFFECT IN WZW BRANES
, 2006
"... The goal of this paper is to give a mathematical treatment of the theory of WZW Dbranes. In particular, we apply (with some changes) the formalism developed in [11] to capturing the WZW Dbrane picture. The theory of WZW branes has several components and has been previously worked out quite satisfa ..."
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The goal of this paper is to give a mathematical treatment of the theory of WZW Dbranes. In particular, we apply (with some changes) the formalism developed in [11] to capturing the WZW Dbrane picture. The theory of WZW branes has several components and has been previously worked out quite satisfactorily physically (see