Grouping by Consecutive Dates and Category

johnfa it was an interesting question, 
you can solve it by copy the below code and past it into the advaance editor.

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("i45WclTSUTIw1AciIwMjEyDHGMGJ1UHIGyPLG2PKm8DkjSzgHJi8kSWSPEixGaZ+C5i8AljYiYCznFBNAtqBZGwsAA==", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type nullable text) meta [Serialized.Text = true]) in type table [Category = _t, #"Start Date" = _t, #"End Date" = _t]),
    #"Changed Type1" = Table.TransformColumnTypes(Source,{{"Category", type text}, {"Start Date", type date}, {"End Date", type date}}),
    #"Grouped Rows" = Table.Group(#"Changed Type1", {"Category"}, {{"Count", each  [a=Table.ToRows(_[[Start Date],[End Date]]),b=List.Accumulate(List.Skip(List.Positions(a)),{1},(x,y)=> if a{y}{0}=a{y-1}{1}+Duration.From(1) then x&{List.Last(x)} else x &{ List.Last(x)+1}), c=Table.AddIndexColumn(_,"in",0,1),d=Table.AddColumn(c,"Grouping",(m)=> b{m[in]})  ][d]}}),
    #"Expanded Count" = Table.ExpandTableColumn(#"Grouped Rows", "Count", {"Category", "Start Date", "End Date", "in", "Grouping"}, {"Category.1", "Start Date", "End Date", "in", "Grouping"})
in
    #"Expanded Count"

Try adding the final parameter to your group step, GroupKind.Local. 

--Nate

Solution 1, concise but requires enough proficiency in PQ,

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("i45WclTSUTIw1AciIwMjEyDHGMGJ1UHIGyPLG2PKm8DkjSzgHJi8kSWSPEixGaZ+C5g8WNSJgKucUA0CWoFkaiwA", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type nullable text) meta [Serialized.Text = true]) in type table [Category = _t, #"Start Date" = _t, #"End Date" = _t]),
    #"Changed Type" = Table.TransformColumnTypes(Source,{{"Category", type text}, {"Start Date", type date}, {"End Date", type date}}, "fr"),
    Rows = Table.ToRecords(#"Changed Type"),
    #"Grouped inner" = List.Transform(List.Accumulate(Rows, {}, (s,c) => if (List.Last(List.Last(s,{}))[Category]? = c[Category]) and (List.Last(List.Last(s))[End Date] + #duration(1,0,0,0) = c[Start Date]) then List.RemoveLastN(s) & {List.Last(s) & {c}} else s & {{c}}), Table.FromRecords),
    #"Extracted Category" = List.Transform(#"Grouped inner", each List.Distinct([Category]){0}),
    #"Grouped outer" = Table.Group(Table.FromColumns({#"Extracted Category", #"Grouped inner"}, {"Category", "grp"}), "Category", {"grp", each Table.AddIndexColumn(_, "Category Index", 1, 1, Int64.Type)}),
    #"Expanded outer" = Table.ExpandTableColumn(#"Grouped outer", "grp", {"grp", "Category Index"}),
    #"Expanded inner" = Table.ExpandTableColumn(#"Expanded outer", "grp", {"Start Date", "End Date"})
in
    #"Expanded inner"

Solution 2, a bit less demanding,

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("i45WclTSUTIw1AciIwMjEyDHGMGJ1UHIGyPLG2PKm8DkjSzgHJi8kSWSPEixGaZ+C5g8WNSJgKucUA0CWoFkaiwA", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type nullable text) meta [Serialized.Text = true]) in type table [Category = _t, #"Start Date" = _t, #"End Date" = _t]),
    #"Changed Type" = Table.TransformColumnTypes(Source,{{"Category", type text}, {"Start Date", type date}, {"End Date", type date}}, "fr"),
    #"Added Index" = Table.AddIndexColumn(#"Changed Type", "Index", 0, 1, Int64.Type),
    #"Added Previous End Date" = let end = #"Added Index"[End Date] in Table.AddColumn(#"Added Index", "Previous End Date", each try end{[Index]-1} otherwise null),
    #"Grouped inner" = Table.Group(#"Added Previous End Date", {"Category","Start Date","Previous End Date"}, {"grp", each _}, 0, (x,y) => Byte.From(x[Category]<>y[Category] or (y[Start Date]<>y[Previous End Date] + #duration(1,0,0,0)))),
    #"Grouped outer" = Table.Group(Table.RemoveColumns(#"Grouped inner",{"Start Date", "Previous End Date"}), "Category", {"grp", each Table.AddIndexColumn(_, "Category Index", 1, 1, Int64.Type)}),
    #"Expanded outer" = Table.ExpandTableColumn(#"Grouped outer", "grp", {"grp", "Category Index"}),
    #"Expanded inner" = Table.ExpandTableColumn(#"Expanded outer", "grp", {"Start Date", "End Date"})
in
    #"Expanded inner"