bundles

(see also Chern-Weil theory, parameterized homotopy theory)

fiber bundles in physics

slice topos, slice (∞,1)-topos

dependent type theory

covering space

fiber bundle, fiber ∞-bundle

numerable bundle

principal bundle, principal ∞-bundle

principal 2-bundle, principal 3-bundle

circle bundle, circle n-bundle

associated bundle, associated ∞-bundle

gerbe, 2-gerbe, ∞-gerbe,

local coefficient bundle

vector bundle, (∞,1)-vector bundle

topological vector bundle, differentiable vector bundle, algebraic vector bundle

Chern-Weil theory

topological K-theory

tensor category of vector bundles

real vector bundle, complex vector bundle

direct sum of vector bundles, tensor product of vector bundles, inner product of vector bundles, dual vector bundle

stable vector bundle

virtual vector bundle

universal principal bundle, universal principal ∞-bundle

universal vector bundle, universal complex line bundle

subobject classifier, object classifier

bundle gerbe

groupal model for universal principal ∞-bundles

microbundle

trivial vector bundle

tangent bundle, normal bundle

tautological line bundle

Hopf fibration

canonical line bundle

prequantum circle bundle, prequantum circle n-bundle

clutching construction

direct sum of vector bundles, tensor product, external tensor product,

inner product on vector bundles

dual vector bundle

projective bundle

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