Algebraic homotopy explained

In mathematics, algebraic homotopy is a research program on homotopy theory proposed by J.H.C. Whitehead in his 1950 ICM talk, where he described it as:^{[1] [2]}

In spirit, the program is somehow similar to Grothendieck's homotopy hypothesis. However, according to Ronnie Brown, "Looking again at Esquisses d'un Progamme, it seems that programme has currently little relation to Whitehead's."^[3]

References

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

Further reading

• https://ncatlab.org/nlab/show/Algebraic+Homotopy, an entry about a book

Notes and References

1. Baues, Homotopy Types in Chapter 1 in Handbook of Algebraic Topology
2. NB: we need a citation to the original source.
3. https://mathoverflow.net/questions/266738/current-status-of-grothendiecks-homotopy-hypothesis-and-whiteheads-algebraic-h