model category, model $\infty$-category
on chain complexes/model structure on cosimplicial abelian groups
related by the Dold-Kan correspondence
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
The category of Delta-generated topological spaces carries the structure of a cofibrantly generated model category with the same generating (acyclic) cofibrations as for the classical model structure on topological spaces and such that the coreflection into all topological spaces (this Prop.) is a Quillen equivalence with the classical model structure on topological spaces:
By the same kind of argument (Gaucher 2007), this factors by a Quillen equivalence through the model structure on compactly generated topological spaces:
Philippe Gaucher, p. 7 of: Homotopical interpretation of globular complex by multipointed d-space, Theory and Applications of Categories, vol. 22, number 22, 588-621, 2009 (arXiv:0710.3553)
Tadayuki Haraguchi, On model structure for coreflective subcategories of a model category, Math. J. Okayama Univ. 57 (2015), 79–84 (arXiv:1304.3622, doi:10.18926/mjou/53040, MR3289294, Zbl 1311.55027)
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