Higher algebra and topological quantum field theory
... maps are bijections. Moreover, it has a left adjoint τ1 , called the fundamental category functor. Proof. The full faithfulness is clear from the above description of the nerve. The existence of an adjoint to the nerve functor follows formally from the completeness of the categories in play (see [GZ ...
... maps are bijections. Moreover, it has a left adjoint τ1 , called the fundamental category functor. Proof. The full faithfulness is clear from the above description of the nerve. The existence of an adjoint to the nerve functor follows formally from the completeness of the categories in play (see [GZ ...
Proposition S1.32. If { Yα} is a family of topological spaces, each of
... rational coordinates is dense. Definition S1.9. A space with a countable dense subset is called separable. Recall that in Rn, a set is compact iff it is closed and bounded. This is known as the Heine-Borel Theorem. It needs to be modified for general pseudometric spaces. A key notion is total bounde ...
... rational coordinates is dense. Definition S1.9. A space with a countable dense subset is called separable. Recall that in Rn, a set is compact iff it is closed and bounded. This is known as the Heine-Borel Theorem. It needs to be modified for general pseudometric spaces. A key notion is total bounde ...
TOPOLOGY ASSIGNMENT 6 CONTINUOUS FUNCTIONS
... (b) Find an example where I is countable and each Ai is closed, but f is not continuous. (c) Find an example where |I| = 2 (that is, X = A1 ∪A2 ), A1 is closed, but f is not continuous. (3) (a) Prove or disprove: Any same cardinaly sets X, Y , equipped with the finite complement topology Tf are home ...
... (b) Find an example where I is countable and each Ai is closed, but f is not continuous. (c) Find an example where |I| = 2 (that is, X = A1 ∪A2 ), A1 is closed, but f is not continuous. (3) (a) Prove or disprove: Any same cardinaly sets X, Y , equipped with the finite complement topology Tf are home ...
Gal(Qp/Qp) as a geometric fundamental group
... It is important to note that a given affinoid ring (R, R+ ) does not necessarily give rise to an adic space Spa(R, R+ ), because the structure sheaf on Spa(R, R+ ) is not necessarily a sheaf. Let us say that (R, R+ ) is sheafy if the structure presheaf on Spa(R, R+ ) is a sheaf. Huber shows (R, R+ ) ...
... It is important to note that a given affinoid ring (R, R+ ) does not necessarily give rise to an adic space Spa(R, R+ ), because the structure sheaf on Spa(R, R+ ) is not necessarily a sheaf. Let us say that (R, R+ ) is sheafy if the structure presheaf on Spa(R, R+ ) is a sheaf. Huber shows (R, R+ ) ...
