Eilenberg-Kelly-MacLane graphs [EK66, KM71] elegantly describe certain morphisms of closed categories. This paper shows that little more is needed to present the free star-autonomous category [Bar79] generated by a category, for a full coherence theorem: the commutativity of diagrams of canonical maps is decidable. Given a set A = {a, b, . . .} of generators, we define the category of A-linking...

In [5] M. Kervaire defined an invariant for (4fc+2)-dimensional framed manifolds. This invariant depends only on the framed bordism class of the manifold and lies in Z2. W. Browder [2] (see also E. H. Brown [3]) gave a generalisation of the invariant that is defined for any even dimensional manifold with a Wu orientation; in this case it depends only on the Wu bordism class. A framed manifold h...

A common theme in algebraic topology is to study functors from the homotopy category of topological spaces to various categories of algebraic objects, such as the classical homology functor, the cohomology functor and the homopoty functor. In this talk, I will introduce some functors from topological spaces to Lie algebras and algebraic varieties, and explore their properties. We can use these ...

We give a functorial construction of equivariant spectra from a generalized version of Mackey functors in categories. This construction relies on the recent description of the category of equivariant spectra due to Guillou and May. The key element of our construction is a spectrally-enriched functor from a spectrally-enriched version of permutative categories to the category of spectra that is ...

Twisted Morava K-theory, along with computational techniques, including a universal coefficient theorem and an Atiyah-Hirzebruch spectral sequence, was introduced by Craig Westerland the first author. We employ these techniques to compute twisted K-theory of all connective covers stable orthogonal group unitary group, their classifying spaces, as well spheres Eilenberg-MacLane spaces. This exte...

We study a variation of Turaev’s homotopy quantum field theories using 2-categories of surfaces. We define the homotopy surface 2-category of a space X and define an SX -structure to be a monoidal 2-functor from this to the 2-category of idempotent-complete additive k-linear categories. We initiate the study of the algebraic structure arising from these functors. In particular we show that, und...

2 Homotopy category of a site with interval 2 2.1 Homotopy theory of simplicial sheaves . . . . . . . . . . . . . . 4 2.1.1 Simplicial sheaves . . . . . . . . . . . . . . . . . . . . . 4 2.1.2 The simplicial model category structure . . . . . . . . 5 2.1.3 Local fibrations and resolution lemmas . . . . . . . . . 8 2.1.4 Homotopy limits and colimits. . . . . . . . . . . . . . . 12 2.1.5 Eilenber...

In this paper, we examine the “derived completion” of the representation ring of a pro-p group G∧ p with respect to an augmentation ideal. This completion is no longer a ring: it is a spectrum with the structure of a module spectrum over the Eilenberg–MacLane spectrum HZ , and can have higher homotopy information. In order to explain the origin of some of these higher homotopy classes, we defin...

In 1993, Henn, Lannes and Schwartz established a very strong relation between the Steenrod algebra and the category F.p/ of functors from the category E of finite dimensional Fp –vector spaces to the category E of all Fp –vector spaces, where Fp is the prime field with p elements [5]. To be more precise, they study the category U of unstable modules over the Steenrod algebra localized away from...