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
model category, model -category
Definitions
Morphisms
Universal constructions
Refinements
Producing new model structures
Presentation of -categories
Model structures
for -groupoids
on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
for equivariant -groupoids
for rational -groupoids
for rational equivariant -groupoids
for -groupoids
for -groups
for -algebras
general -algebras
specific -algebras
for stable/spectrum objects
for -categories
for stable -categories
for -operads
for -categories
for -sheaves / -stacks
The notion of homotopy pushout is
the generalization of the notion of pushout to homotopy theory, hence from 1-category-category theory to -category theory, and here often understood as a derived functor of the pushout-functor
the formal dual to the notion of homotopy pullback. For the moment, see there for more details.
Homotopy pushouts are at least mentioned in essentially any textbook on homotopy theory.
Dedicated textbook introductions:
Jeffrey Strom, Homotopy Pushout Squares, §7.1 in: Modern classical homotopy theory, Graduate Studies in Mathematics 127, American Mathematical Society (2011) [doi:10.1090/gsm/127]
Martin Arkowitz, Homotopy Pushouts and Pullbacks, §6 in: Introduction to Homotopy Theory, Springer (2011) [doi:10.1007/978-1-4419-7329-0]
Peter May, Kate Ponto, Some basic homotopy colimits, §2.1 in: More concise algebraic topology, University of Chicago Press (2012) [ISBN:9780226511795, pdf]
For more references see at
Last revised on September 27, 2026 at 05:44:21. See the history of this page for a list of all contributions to it.