E(N)-MONOIDAL CATEGORIES AND THEIR GROUP-COMPLETIONS

[摘要] An E(n)-monoidal structure on a category A is a coherently associative and commutative multiplication on A with respect to which the classifying space BA has an n-fold delooping. When n = 1, 2 or infinity an E(n)-monoidal structure is, up to equivalence, a strict monoidal, braided tensor or permutative structure respectively. The construction of deloopings requires a careful analysis of higher homotopy commutativity for E(n)-monoidal categories A. There results a category W A such that BW A is an n-fold delooping of BA. We also construct an n-fold delooping of A as a sequence of 1-fold deloopings.

[发布日期] 1994-07-25