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We present a short overview of the TeV-Halos objects as a discovery and arelevant contribution of the High Altitude Water \v{C}erenkov (HAWC)observatory to TeV astrophysics. We discuss history, discovery, knowledge, andthe next step through a new and more detailed analysis than the original studyin 2017. TeV-Halos will contribute to resolving the problem of the localpositron excess observed on the Earth. To clarify the latter, understanding thediffusion process is mandatory.

A Contribution of the HAWC Observatory to the TeV era in the High Energy Gamma-Ray Astrophysics: The case of the TeV-Halos