Commutative Algebra and its Interactions A conference in honor of Mel Hochster July 31 - August 5, 2008 Abstract Detail   Title: Grothendieck operations and coherence in categories I will illustrate the yoga of Grothendieck Duality, in the scaled-down context of modules over rings and quasi-finite ring homomorphisms. The emphasis will be on basic category-theoretic properties of familiar maps, thought of as relations among Grothendieck operations (tensor, hom, restriction and extension of scalars); and on the need to deduce commutativity of many natural diagrams from these "axiomatic" properties. (The problem, purely formal, is no different for full-blown Grothendieck Duality, in the context of derived categories over noetherian schemes and separated finite-type scheme-maps.) The resulting overwhelming tedium issues a challenge: fight back with some form of automated reasoning, or better, with general theorems. This is the stuff of coherence in categories. Joseph Lipman Purdue University Email:  jlipman@purdue.edu Phone: 765-494-1994   BACK to Speaker Listing BACK to Conference Home