Publication

Conditionally flat functors on spaces and groups

Jérôme Scherer
2015
Journal Articles

Abstract

Consider a fibration sequence of topological spaces which is preserved as such by some functor , so that is again a fibration sequence. Pull the fibration back along an arbitrary map into the base space. Does the pullback fibration enjoy the same property? For most functors this is not to be expected, and we concentrate mostly on homotopical localization functors. We prove that the only homotopical localization functors which behave well under pull-backs are nullifications. The same question makes sense in other categories. We are interested in groups and how localization functors behave with respect to group extensions. We prove that group theoretical nullification functors behave nicely, and so do all epireflections arising from a variety of groups.

Official source

https://infoscience.epfl.ch/entities/publication/456121e4-fd8b-45ba-8a6c-f31cf9024ba3

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Jérôme Scherer
2015
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/456121e4-fd8b-45ba-8a6c-f31cf9024ba3

About this result

Related concepts (32)

Functor

In mathematics, specifically , a functor is a mapping between . Functors were first considered in algebraic topology, where algebraic objects (such as the fundamental group) are associated to topological spaces, and maps between these algebraic objects are associated to continuous maps between spaces. Nowadays, functors are used throughout modern mathematics to relate various categories. Thus, functors are important in all areas within mathematics to which is applied.

Pointed space

In mathematics, a pointed space or based space is a topological space with a distinguished point, the basepoint. The distinguished point is just simply one particular point, picked out from the space, and given a name, such as that remains unchanged during subsequent discussion, and is kept track of during all operations. Maps of pointed spaces (based maps) are continuous maps preserving basepoints, i.e.

Adjoint functors

In mathematics, specifically , adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between two related categories. Two functors that stand in this relationship are known as adjoint functors, one being the left adjoint and the other the right adjoint. Pairs of adjoint functors are ubiquitous in mathematics and often arise from constructions of "optimal solutions" to certain problems (i.e.

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Conditionally flat functors on spaces and groups

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