134 research outputs found
On the braiding of an Ann-category
A braided Ann-category \A is an Ann-category \A together with the
braiding such that (\A, \otimes, a, c, (I,l,r)) is a braided tensor
category, and is compatible with the distributivity constraints. The paper
shows the dependence of the left (or right) distributivity constraint on other
axioms. Hence, the paper shows the relation to the concepts of {\it
distributivity category} due to M. L. Laplaza and {\it ring-like category} due
to A. Frohlich and C.T.C Wall.
The center construction of an almost strict Ann-category is an example of an
unsymmetric braided Ann-category.Comment: 20 page
An involution on the K-theory of bimonoidal categories with anti-involution
We construct a combinatorially defined involution on the algebraic -theory
of the ring spectrum associated to a bimonoidal category with anti-involution.
Particular examples of such are braided bimonoidal categories. We investigate
examples such as algebraic K-theory of connective complex and real topological
K-theory and Waldhausen's K-theory of spaces of the form BBG, for abelian
groups G. We show that the involution agrees with the classical one for a
bimonoidal category associated to a ring and prove that it is not trivial in
the above mentioned examples
Weakly distributive categories
AbstractThere are many situations in logic, theoretical computer science, and category theory where two binary operations — one thought of as a (tensor) “product”, the other a “sum” — play a key role. In distributive and ∗-autonomous categories these operations can be regarded as, respectively, the and/or of traditional logic and the times/par of (multiplicative) linear logic. In the latter logic, however, the distributivity of product over sum is conspicuously absent: this paper studies a “linearization” of that distributivity which is present in both case. Furthermore, we show that this weak distributivity is precisely what is needed to model Gentzen's cut rule (in the absence of other structural rules) and can be strengthened in two natural ways to generate full distributivity and ∗-autonomous categories
Operads within monoidal pseudo algebras
A general notion of operad is given, which includes as instances, the operads
originally conceived to study loop spaces, as well as the higher operads that
arise in the globular approach to higher dimensional algebra. In the framework
of this paper, one can also describe symmetric and braided analogues of higher
operads, likely to be important to the study of weakly symmetric, higher
dimensional monoidal structures
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