Summary: INTERNAL CATEGORIES AND QUANTUM GROUPS
Presented to the Faculty of the Graduate School
of Cornell University
in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
INTERNAL CATEGORIES AND QUANTUM GROUPS
Marcelo Aguiar, Ph.D.
Cornell University 1997
Let S be a monoidal category with equalizers that are preserved by the tensor
product. The notion of categories internal to S is defined, generalizing the notions
of monoid and comonoid in S, and extending the usual notion of internal categories,
which is obtained when S is a category with products and equalizers.
The basic theory of internal categories is developed and several applications to
quantum groups are found. Deltacategories are defined; these are algebraic objects
that generalize groups or bialgebras, in the sense that attached to them there is
a monoidal category of representations. Quantum groups are constructed from