# nLab Peter May

J. Peter May is a homotopy theorist at the University of Chicago, inventor of operads as a technique for studying infinite loop spaces and spectra.

Peter May’s work makes extensive use of enriched- and model-category theory as power tools in algebraic topology/homotopy theory, notably in discussion of highly structured spectra in MMSS00‘s Model categories of diagram spectra (for exposition see Introduction to Stable homotopy theory – 1-2), or in the discussion of genuine equivariant spectra or K-theory of permutative categories, etc.. While he has co-edited a book collection on higher category theory (Baez-May 10) and eventually had high praise (May 16) for 2-category theory as a tool in algebraic topology/higher algebra, he has vocally warned against seeing abstract (∞,1)-category theory as a replacement for concrete realizations in model category-theory (P. May, MO comment Dec 2013).

## Selected writings

• Peter May, The geometry of iterated loop spaces, 1972 (pdf)

• Peter May, Infinite loop space theory, Bull. Amer. Math. Soc. Volume 83, Number 4 (1977), 456-494. (Euclid)

Infinite loop space theory revisited (pdf)

On higher algebra (brave new algebra) in stable homotopy theory, i.e. on ring spectra, module spectra etc.:

• Peter May, Equivariant and non-equivariant module spectra, Journal of Pure and Applied Algebra Volume 127, Issue 1, 1 May 1998, Pages 83–97 (pdf)