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...

Homotopy theory studies topological spaces up to homotopy, so it must study the functor π∗ : Top → Π−algebras. Passage to the homotopy category is declaring π∗-isomorphisms to be isomorphisms. Because this functor is difficult to compute, one way to do homotopy theory is to study simpler functors which also map to graded abelian categories, e.g. πQ ∗ , H∗(−;Z), K∗, or more generally E∗ for E so...

In this paper a binary relation between L-sets, called attachment, is defined by means of a suitable family of completely coprime filters in L. Examples are given using several kinds of lattice-ordered algebras and a class of attachments is determined whose elements generalize Pu-Liu’s quasi-coincidence relation. Mapping any L-set on X to the set of the attached L-points one gets a frame map fr...

Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.

The process of inverting Markov kernels relates to the important subject of Bayesian modelling and learning. In fact, Bayesian update is exactly kernel inversion. In this paper, we investigate how and when Markov kernels (aka stochastic relations, or probabilistic mappings, or simply kernels) can be inverted. We address the question both directly on the category of measurable spaces, and indire...

The process of inverting Markov kernels relates to the important subject of Bayesian modelling and learning. In fact, Bayesian update is exactly kernel inversion. In this paper, we investigate how and when Markov kernels (aka stochastic relations, or probabilistic mappings, or simply kernels) can be inverted. We address the question both directly on the category of measurable spaces, and indire...

For a quantaloid Q, considered as a bicategory, Walters introduced categories enriched in Q. Here we extend the study of monad-quantale-enriched categories of the past fifteen years by introducing monad-quantaloid-enriched categories. We do so by making lax distributive laws of a monad T over the discrete presheaf monad of the small quantaloid Q the primary data of the theory, rather than the l...

Twisted topological Hochschild homology of Cn-equivariant spectra was introduced by Angeltveit, Blumberg, Gerhardt, Hill, Lawson, and Mandell, building on the work Hopkins, Ravenel norms in equivariant homotopy theory. In this paper we introduce tools for computing twisted THH, which apply to computations Thom spectra, Eilenberg-MacLane real bordism spectrum MUR. particular, construct an versio...

Goodwillie’s calculus of homotopy functors associates a tower of polynomial approximations, the Taylor tower, to a functor of topological spaces over a fixed space. We define a new tower, the varying center tower, for functors of categories with a fixed initial object, such as algebras under a fixed ring spectrum. We construct this new tower using elements of the Taylor tower constructions of B...