We propose a simplified definition of Quillen’s fibration sequences in pointed model category that fully captures the theory, although it is completely independent concept action. This advantage arises from understanding homotopy

Homotopy theory deals with spaces of large but finite dimension. Chromatic homotopy theory is an organizing principle which is highly developed in the stable situation. 1. The Spanier-Whitehead category. We'll work with the category of finite polyhedra (or finite CW complexes) and homotopy classes of continuous maps between them. We will always fix a basepoint in all spaces, and assume that map...

The notion of cofiber sequence is dual to that of fiber sequence. Most constructions and statements about fiber sequences readily dualize to cofiber sequences, though there are differences to be mindful of. 1. Fiber sequences were defined in the category of pointed spaces Top * , so that taking the strict fiber (i.e. preimage of the basepoint) makes sense. No such restriction exists for cofiber...

The categorical definition of semidirect products was introduced by D. Bourn and G. Janelidze in [2], where they proved that, in the category of groups, this notion coincides with the classical one. A characterization of pointed categories with categorical semidirect products was given in [3]. The existence of such products imply, in particular, that the category is protomodular, i.e. the Split...

The general methodology of “algebraizing” logics (cf. [2], [4]) is used here for combining different logics. The combination of logics is represented as taking the colimit of the constituent logics in the category of algebraizable logics. The cocompleteness of this category as well as its isomorphism to the corresponding category of certain first-order theories are proved. In this paper we tran...

We develop the K-theory of sets with an action a pointed monoid (or scheme), analogous to modules over ring scheme). In order form localization sequences, we construct quotient category nice regular by Serre subcategory.

Let g and n be nonnegative integers A = ( a 0 , … ) sequence of + 1 summing up to d . M ? the moduli space -pointed stable curves genus J ? ? Esteves' universal Jacobian, where is genus- polarization degree We give an explicit resolution Abel map ? : ? taking pointed curve X p O ? ? i The blowup giving rise inspired by tropical analogue (in category generalized cone complexes). As application, ...