JQ: Remove object from multiple arrays - arrays

Question

I want to use jq to remove all objects with a given name from all arrays in the input data. For example deleting "Name1" from this:
{
"Category1": [
{
"name": "Name1",
"desc": "Desc1"
},
{
"name": "Name2",
"desc": "Desc2"
}
],
"Category2": [
{
"name": "Name1",
"desc": "Desc1"
},
{
"name": "Name3",
"desc": "Desc3"
}
],
"Category3": [
{
"name": "Name4",
"desc": "Desc4"
}
]
}
Should yield this:
{
"Category1": [
{
"name": "Name2",
"desc": "Desc2"
}
],
"Category2": [
{
"name": "Name3",
"desc": "Desc3"
}
],
"Category3": [
{
"name": "Name4",
"desc": "Desc4"
}
]
}
I haven't worked with jq, or indeed JSON, much and after several hours of googling and experimenting I haven't been able to figure it out. How would I do this?
The closest I managed was this:
cat input | jq 'keys[] as $k | .[$k] |= map( select( .name != "Name1"))'
This does filter each of the arrays but returns the result as three separate objects and this is not what I want.

Answer 1

If the structure of your input JSON is always as seen on your example, try this:
map_values(map(select(.name != "Name1")))

Answer 2

Here is a solution that will remove all objects with the specified name, wherever they occur. It uses the generic function walk/1,
which is a built-in in versions of jq > 1.5, and can therefore be omitted if your jq includes it, but there is no harm in including it redundantly, e.g. in a jq script.
# Apply f to composite entities recursively, and to atoms
def walk(f):
. as $in
| if type == "object" then
reduce keys[] as $key
( {}; . + { ($key): ($in[$key] | walk(f)) } ) | f
elif type == "array" then map( walk(f) ) | f
else f
end;
walk(if type == "object" and .name == "Name1" then empty else . end)
If you really only want to remove objects from arrays, then you could use:
walk(if type == "array" then map(select( type != "object" or .name != "Name1")) else . end)

Answer 3

Here is a solution which uses reduce and del
reduce keys[] as $k (
.
; del(.[$k][] | select(.name == "Name1"))
)