In mathematics, algebraic homotopy is a research program on

homotopy theory In mathematics, homotopy theory is a systematic study of situations in which Map (mathematics), maps can come with homotopy, homotopies between them. It originated as a topic in algebraic topology, but nowadays is learned as an independent discipli ...

proposed by

J.H.C. Whitehead John Henry Constantine Whitehead Fellow of the Royal Society, FRS (11 November 1904 – 8 May 1960), known as "Henry", was a British mathematician and was one of the founders of homotopy theory. He was born in Chennai (then known as Madras), i ...

in his 1950 ICM talk, where he described it as: In spirit, the program is somehow similar to Grothendieck's

homotopy hypothesis In category theory, a branch of mathematics, Grothendieck's homotopy hypothesis states, homotopy theory speaking, that the ∞-groupoids are space (mathematics), spaces. One version of the hypothesis was claimed to be proved in the 1991 paper by M ...

. However, according to Ronnie Brown, "Looking again at Esquisses d'un Progamme, it seems that programme has currently little relation to Whitehead's."https://mathoverflow.net/questions/266738/current-status-of-grothendiecks-homotopy-hypothesis-and-whiteheads-algebraic-h

References

* https://ncatlab.org/nlab/show/algebraic+homotopy
Handbook of Algebraic Topology
edited by I.M. James

References

Further reading