Talk:Locally constant sheaf

Is the locally connected assumption necessary?

I recently noticed during an Algebraic Topology lecture that the proof of the equivalence between the categories of covering spaces and locally constant sheaves of sets does not require the assumption of local connectedness. When I looked at the original reference for this, an exercise in Sheaves in Geometry and Logic by Mac Lane and Moerdijk, it used a very weird definition of locally constant and the actual equivalence was never stated anywhere, so I added a reference to Galois Groups and Fundamental Groups by Tamás Szamuely. Sadly the proof in this book also assumes local connectedness, but this assumption appears to be unnecessary. The nlab pages on this topic also never put any assumption on the topological space. Does anyone know of a good source/reference with a proof that does not assume local connectedness? CodingDragon04 (talk) 09:19, 15 June 2023 (UTC)