215 research outputs found
On the PROP corresponding to bialgebras
A PROP is a symmetric monoidal category, whose set of objects is the set of
natural numbers and on objects the monoidal structure is given by the addition.
An algebra over a PROP is a symmetric strict monoidal functor to the tensor
category of vector spaces. We give an explicite construction of the PROP whose
category of algebras is equivalent to the category of bialgebras (= associative
and coassociative bialgebras)
Andr\'e-Quillen homology via functor homology
We obtain Andr\'e-Quillen homology for commutative algebras using relative
homological algebra in the category of functors on finite pointed set
On the equvialence of colimits and 2-colimits
We compare the colimit and 2-colimit of strict 2-functors in the 2-category
of groupoids, over a certain type of posets. These posets are of special
importance, as they correspond to coverings of a topological space. The main
result of this paper gives conditions on the 2-functor , for
which . One can
easily see that any 2-functor can be deformed to a 2-functor
, which satisfied the conditions of the theorem
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