homotopy theory, (∞,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…
models: topological, simplicial, localic, …
see also algebraic topology
Introductions
Definitions
Paths and cylinders
Homotopy groups
Basic facts
Theorems
This page collects material related to the textbook
Simplicial homotopy theory,
Progress in Mathematics, Birkhäuser (1999)
Modern Birkhäuser Classics (2009)
(web) (ps and dvi only - note that section and theorem etc numbers differ from the published version!)
on simplicial homotopy theory via the classical model structure on simplicial sets.
There is also an article by E. B. Curtis with this name, from 1971.
We list the notions explained in the book for searchability.
Alexander-Whitney map, almost free morphism, anodyne extension, barycentric subdivision, bisimplex, bisimplicial abelian group, bisimplicial set, bonding map, Bousfield factorization, Bousfield-Kan R-completion, Bousfield-Kan R-resolution, G-bundle, category translation, resolution of a category, classifying object, classifying space, closed n-loop, model structure (Reedy, Moerdijk, f-local, Q-structure, cofibrantly generated, stable, strict, towers), cocycle, codegeneracy, coface, coglueing lemma, cohomotopy groups, pointed cone, continuous functor, coskeleton, covering system, equivariant Dold-Kan correspondence, Dwyer-Kan theorem, $Ex^{\infty}$ functor, Ext-p complete groups, Eilenberg subcomplex, Eilenberg-Zilber theorem, endpoint preserving, equivariant cohomology, expontial law, extension condition, external product, extra degeneracy, f-injective map, f-local space, f-localization, various kinds of fibration (Reedy, Serre, Q-fibration, acyclic, diagonal, global, minimal, pointwise, principal, stable, strict), Freudenthal suspension theorem, fringed spectral sequence, function complex, glueing lemma, Grothendieck construction, group completion, free groupoid, fundamental groupoid, homotopically full and faithful, homotopy cartesian, homotopy coherent diagram, homotopy colimit, homotopy fibre sequence, homotopy inverse limit, homotopy left Kan extension, homotopy pullback, homotopy spectral sequence (for a cosimplicial space, for a homotopy inverse limit, of a tower), horisontal normalization, horn, Hurewicz map, Hurewicz theorem, interchange law, join functor, k-invariant, Kan complex, Kan extension, Kan suspension, latching object, lax functor, left homotopy, local coefficient system, loop group, loop groupoid, loop spectrum, fake loop spectrum, loop space, matching object, matching space, Milnor FK-construction, Milnor exact sequence, Moore complex, Moore bicomplex, Moore-Postnikov section, Moore-Postnikov tower, nilpotent space, p-completion of a space, p-completion of an abelian group, Postnikov section, Postnikov tower, projective generator, pseudo cross-section, quasi-isomorphism, realization, n-reduced, relative homotopy group, retract, right lifting property, saturated, segment, Serre spectral sequence, shuffle map, simplical [abelian gruop, algebra, category, circle, coalgebra, functor, graded algebra, graded module, group, group action, groupoid, homotopy, map, model category, module, presheaf], simplicial set (n-fold, n-truncated, diagonal, reduced), singular set, skeleton, small object argument, spectrum, stable category, suspension ,Theorem B, total derived functor theorem, transgression, translation object, tree, trisimplicial set, universal cover, unstable algebra, van Kampen theorem, vertical path component, vertical simplicial set, weak equivalence, f-local equivalence, Q-weak equivalence, pointwise WE, Reedy WE, stable equivalence, strict WE of spectra, weak r-equivalence.