It is well-known that gauging a finite 0-form symmetry in quantum field theory leads to dual generated by topological Wilson line defects. These are described the representations of group which form 1-category. We argue for d-dimensional full set symmetries one obtains fact much larger and (d-1)-category, formed out lower-dimensional theories with same symmetry. study detail 2-categorical piece...

hold. If such matrix X exists, then it is unique, denoted by A, and called the group inverse of A. It is well known that the group inverse of a square matrix A exists if and only if rank(A) = rank(A) (see, for example, [1, Section 4.4] for details). Clearly, not every matrix is group invertible. It is straightforward to prove that A is group invertible if and only if A is group invertible, and ...

In normal version of combinatorial game theory, all games are invertible, whereas only the empty game is invertible in misère version. For this reason, several restricted universes were earlier considered for their study, in which more games are invertible. We here study combinatorial games in misère version, in particular universes where no player would like to pass their turn In these univers...

The invertible deoxyribonucleic acid (DNA) segment cloned from Salmonella sp. was radioactively labeled and used as a probe to search for homologous sequences by Southern hybridization. Only one copy of the invertible segment could be found on the Salmonella sp. genome. Partial sequence homology with the invertible region was detected in bacteriophage Mu and P1 DNA by low-stringency hybridizati...

For operators of many different kinds it has been proved that (generalized) Darboux transformations can be built using so called Wronskian formulae. Such Darboux transformations are not invertible in the sense that the corresponding mappings of the operator kernels are not invertible. The only known invertible ones were Laplace transformations (and their compositions), which are special cases o...

A linear 2-All-or-Nothing Transform can be considered as an invertible matrix with all 2 × 2 submatrices invertible. It is known [P. D’Arco, N. Nasr Esfahani and D.R. Stinson, Electron. J. Combin. 23(4) (2016), #P4.10] that there is no binary s×s matrix that satisfies these conditions, for s > 2. In this paper, different computational methods for generating invertible binary matrices with close...