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What are the potential uses and misuses of applying category theory to the study of consciousness? We first review a new study from the neurosciences of consciousness to illustrate the general approach taken by using the integrated information theory of consciousness. A better understanding of mindfulness cannot be obtained by simply investigating the physical brain.
Source link: https://doi.org/10.31234/osf.io/3vhg9
We extend undirected graph methods to directed graph contexts by converting directed graphs from directed graphs by converting the directed graphs to prime graphs, benefiting from the isomorphism between these two groups.
Source link: https://doi.org/10.21203/rs.3.rs-1995489/v2
In this sense, designing a u2019bridge u2019 that connects directed graphs to undirected graphs will open the possibility of using undirected graph techniques in appropriate directed graph contexts. We used Category Theory in a novel way to map a simple directed graph to a bipartite undirected graph that we'll refer to as a prime graph. We extend undirected graph methods to directed graph contexts by converting the directed graphs into prime graphs by utilizing the isomorphism between these two categories.
Source link: https://doi.org/10.21203/rs.3.rs-1995489/v1
A bstract We investigate a 4d gauge theory U N2212 1 u2212 1 u2212 1 U2212 1 theory by gauging a 0-form symmetry S N based on a U N2112 1 model. We find a map with gauge invariant operators of 4d SU Yang-Mills theory by investigating the characteristics of local and extended operators. A 2̆124_N^(1) N 1 1-form symmetry is the most significant subcategory of our theory's non-invertible symmetries of our theory, and it functions on the Wilson lines in the same way as Yang-Mills' center symmetry does.
Source link: https://doi.org/10.1007/jhep12(2022)061
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