Some aspects of topological descent

The paper deals with (effective) descent morphisms for subfibrations #IOTA##EPSILON#(#CHI#) of the basic fibration #TAU#op/#CHI#, for topological spaces #CHI# and classes #IOTA##EPSILON# of continuous functions stable under pullback. For a category with pullbacks, we prove the stability under pullback of effective #IOTA##EPSILON#-descent morphisms for a class #IOTA##EPSILON# satisfying some conditions. This plays a role in relating effective#IOTA##EPSILON#-descent to effective global descent and enables us to obtain a criterion for effective etale-descent. We also show that the the inclusion of the class of surjective effective etale-descent is strictAvailable from Departamento de Matematica, Universidade de Coimbra, 3000 Coimbra, Portugal / FCT - Fundação para o Ciência e a TecnologiaSIGLEPTPortuga