Xiuzhan Guo - Remarks on descent theory

(Joint work with Walter Tholen)

A theorem of Joyal and Tierney states that, analogously to the result for commutative rings, a morphism in the opposite of the category of commutative monoids is effective for descent iff it is a pure monomorphism (Mem. Amer. Math. Soc. 309). Based on these results, in this talk, we shall discuss several new directions for descent theory.