We have shown that the n–th Morava K –theory K∗(X) for a CW–spectrum X with action of Morava stabilizer group Gn can be recovered from the system of some height–(n + 1) cohomology groups E∗(Z) with Gn+1 –action indexed by finite subspectra Z . In this note we reformulate and extend the above result. We construct a symmetric monoidal functor F from the category of E∨ ∗ (E)–precomodules to the ca...

introduction exposure to chronic levels of ionizing radiation could be detrimental to health even at very low doses. calabar free trade zone (cftz) was established to promote export business in nigeria and it is yet to produce exposure data of the zone. materials and methods the zone was divided into three categories depending on the type of business. category a had facilities with manufacturin...

There is a very close and well-understood relationship between proofs in intuitionistic logic, simply typed lambda-terms, and morphisms in Cartesian closed categories. The same relationship can be established for multiplicative linear logic (MLL), where proof nets take the role of the lambda-terms, and starautonomous categories the role of Cartesian closed categories. It is certainly desirable ...

In this paper we offer a solution to the long-standing problem of group completing within the context of rig categories (also known as bimonoidal categories). More precisely, given a rig category R we construct a natural additive group completion R̄ of R that retains the multiplicative structure, meaning that it remains a rig category. In other words, it has become a ring category. If we start w...

The most familiar example of higher, or vertically iterated enrichment is that in the definition of strict n-category. We begin with strict n-categories based on a general symmetric monoidal category V. Motivation is offered through a comparison of the classical and extended versions of topological quantum field theory. A sequence of categorical types that filter the category of monoidal catego...

Michael Neumann t Department of Mathematics University of Connecticut . Storrs, CT 06269-3009. Because the spectral radius is only an asymptotic measure of the rate of convergence of a linear iterative method, Golub and dePillis have raised in a recent paper the question of determining, for each k ~ 1, a relaxation parameter w E (0,2) and a pair of relaxation parameters WI and W2 which minimize...

The subject of linear logic has recently become very important in theoretical computer science. It is apparent that the ∗-autonomous categories studied at length in [Barr, 1979] are a model for a large fragment of linear logic, although not quite for the whole thing. Since the main reference is out of print and since large parts of that volume are devoted to results highly peripheral to the mat...

In this paper we show how to write any variety over a field of characteristic zero as the difference of two pure motives, thus answering a question asked by Serre (in arbitrary characteristic, [Se] p.341). The Grothendieck theory of (pure effective Chow) motives starts with the category V of smooth projective varieties over a field k. A motive is a pair (X, p), where X is in V and p is a projec...

The 2-category VAR of finitary varieties is not varietal over CAT . We introduce the concept of an algebraically exact category and prove that the 2-category ALG of all algebraically exact categories is an equational hull of VAR w.r.t. all operations with rank. Every algebraically exact category K is complete, exact, and has filtered colimits which (a) commute with finite limits and (b) distrib...