Joseph Lipman

Purdue University, EE.UU.

“Grothendieck operations and coherence in categories”

Resumen: 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 di fferent 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 stu ff

of coherence in categories.