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
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A quasifibration is a kind of fibration, a morphism in homotopy theory that acts like a fibration in that the actual fibres are, via the canonical inclusions, weakly homotopy equivalent to the homotopy fibres (note that no lifting properties are used in the definition). As a result the long exact sequence in homotopy for the replacement of the map by a fibration becomes an long exact sequence for the map itself.
For variations on the definition and some history, see
Also see
Last revised on February 15, 2019 at 14:53:33. See the history of this page for a list of all contributions to it.