Deformations of coalgebra morphisms

Deformations of Coalgebra Morphisms

An algebraic deformation theory of coalgebra morphisms is constructed.

Coalgebra-to-Algebra Morphisms

Given a coalgebra p for HG, an algebra s for GH and the obvious notion of morphism from coalgebra to algebra, we observe that morphisms from Gp to s correspond to morphisms from p to Hs in the manner of an adjunction even when there is no adjunction between G and H. This appears to be one of the basic phenomena underlying the transport of special algebras. A proof of Freyd’s Iterated Square The...

Coalgebra Morphisms Subsume Open Maps

Formal Deformations of Morphisms of Associative Algebras

The L∞-algebra controlling simultaneous deformations of a morphism of associative algebras and its domain and codomain is described. Isomorphism of the cohomology of this L∞-algebra with the classical construction is shown.

Infinitesimal Deformations of Harmonic Maps and Morphisms

Harmonic maps are mappings between Riemannian manifolds which extremize a natural energy functional. They have been studied for many years in differential geometry, and in particle physics as nonlinear sigma models. We shall report on recent progress in understanding their infinitesimal deformations, the so-called Jacobi fields. It is important to know whether the Jacobi fields along harmonic m...