Injectivity is an important concept in algebra, homotopy theory and elsewhere. We study the ‘injectivity consequence’ of morphisms of a category: a morphism h is a consequence of a set H of morphisms if every object injective w.r.t. all members of H is also injective w.r.t. h. We formulate a very simple logic which is always sound, i.e., whenever a proof of h from assumptions in H exists, then ...

Après avoir transféré au cadre différentiable la notion algébrique d’équivalence de groupöıdes, nous montrons que les morphismes de la catégorie de fractions correspondante sont représentés par une unique fraction irréductible (calcul de fractions simplifié) que nous identifions aux morphismes de Connes–Skandalis–Haefliger entre espace de feuilles. Dans cette catégorie de fractions, le groupe f...

Let H be a quasi-Hopf algebra. We show that any H-bimodule coalgebra C for which there exists an H-bimodule coalgebra morphism ν : C → H is isomorphic to what we will call a smash product coalgebra. To this end, we use an explicit monoidal equivalence between the category of two-sided two-cosided Hopf modules over H and the category of left Yetter-Drinfeld modules over H. This categorical metho...

The aim is the theorems of the title and the corollary that the tensor product of two free crossed resolutions of groups or groupoids is also a free crossed resolution of the product group or groupoid. The route to this corollary is through the equivalence of the category of crossed complexes with that of cubical ω-groupoids with connections where the initial definition of the tensor product li...

THEOREM I. Let X be a small category. Then the following assertions are equivalent: (1) The inverse limit proj limx: AB-^AB is exact (2) For every abelian category SÏ with exact direct products y the inverse limit proj lim* : %—»3I is exact. (3) Every connected component Y of X contains an object y together with an endomorphism eÇz Y (y, y) such that the following properties are satisfied: (i) ...

To a B-coring and a (B, A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule such as separability and the Frobenius properties are reflected in the induced base ring extension coring. Any bimodule that is finitely generated and projec...

  Background: Routine repeat testing of critical laboratory values is very common these days to increase their accuracy and to avoid reporting false or infeasible results. We figure that repeat testing of critical laboratory values has any benefits or not.   Methods : We examined 2233 repeated critical laboratory values in 13 different hematology and chemistry tests including: hemoglobin, white...

We show that the class of weak equivalences of a combinatorial model category can be detected by an accessible functor into simplicial sets. The purpose of this short note is to prove the following result that was conjectured by J.H. Smith in [[2],p. 460]. 0.1. Theorem. For every combinatorial model categoryM, there is an accessible functor F :M→ SSet that detects the weak equivalences, i.e., a...