Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finitistic Dimension of Faithfully Flat Weak Hopf-Galois Extension   Let $H$ be a finite-dimensional weak Hopf algebra over a field $k$ and $A/B$
be a right faithfully flat weak $H$-Galois extension. We prove that if the
finitistic dimension of $B$ is finite, then it is less than or equal to that of
$A$. Moreover, suppose that $H$ is semisimple. If the finitistic dimension
conjecture holds, then the finitistic dimension of $B$ is equal to that of $A$.

35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin