Can a product belong to two categories?

In the navigation taxonomy, yes, and it usually should. In the master product taxonomy, no. One SKU, one master node. If a product genuinely seems to belong in two master nodes, the node definitions overlap and one of them needs to be redrawn.

How deep should a product taxonomy go?

Deep enough that every node has a distinct required attribute set, and no deeper. If two adjacent leaf nodes require identical attributes and behave identically in merchandising, they are one node with an attribute distinguishing them. Depth beyond four or five levels is usually attributes that were modeled as hierarchy.

Does a PIM enforce this separation automatically?

No. Every major PIM supports multiple hierarchies, and none of them decides which one is authoritative for setup. That decision is yours, and it has to be written down and enforced in workflow, or the structures will drift back together within a year.

What does this have to do with AI search?

An assistant answering "which dog bowls are dishwasher safe and under $30" is doing attribute filtering, not category browsing. Catalogs whose meaning lives in attributes answer that question. Catalogs whose meaning lives in category names cannot, because the category name is not machine-readable data about the product.

Product taxonomy vs. navigation taxonomy

A product taxonomy assigns every SKU to exactly one node, so the business has one unambiguous place to set it up, count it and report on it. A navigation taxonomy places that same SKU wherever customers would look for it, which is often several places at once. They are different structures serving different masters, and merging them is the single most common catalog architecture mistake.

Why the two get merged

The merge happens for a defensible reason. When a catalog is small, one tree can serve everyone: merchants set products up in it, the website renders it as navigation, and finance reports off it. Nobody has to reconcile anything. The structure only breaks when three groups start pulling it in different directions.

Merchants want a tree that mirrors how they buy, because that is how their budget and their vendor relationships are organized. Finance wants a tree that rolls up cleanly to a P&L, which means nothing may appear twice. Customers want to find a stainless steel dog bowl by searching for a dog bowl, by browsing Dog to Feeding, by filtering Material = Stainless Steel, and increasingly by asking an assistant a question in plain language. Those are four different access paths to one SKU.

A single tree can satisfy any two of those three groups. It cannot satisfy all three. What usually happens is that the customer view wins, because the website is visible and the reporting is not, and the master structure fills with marketing categories that nobody can report on.

The three structures worth maintaining

In practice a mature catalog carries three related structures, not one:

Master product taxonomy (1:1). Every SKU sits in exactly one node. This is the setup structure: it drives required attributes, workflow routing, data validation, and who owns the record. If a SKU appears twice here, your attribute requirements and your ownership model are both ambiguous.
Web navigation taxonomy (1:many). Customer-facing. A SKU qualifies for as many nodes as make sense. This is the structure that gets rebuilt every time the site is redesigned, which is exactly why it must not be the setup structure.
Merchant or financial taxonomy (1:1, different shape). Rolls up to the way the business is bought and reported. Frequently similar to the master taxonomy but not identical, because buying teams reorganize and reporting history has to stay comparable.

An attribute-driven selling taxonomy sits on top of all three: it is not a tree at all, but a set of filters that assemble a temporary category from attributes on demand. Most of what customers experience as “categories” on a modern site should be produced this way.

Connecting them with rules, not with mapping tables

The instinct is to build a mapping table: master node A appears in web nodes B, C and D. That works until the catalog grows, at which point the table becomes a second full-time job and quietly goes stale.

The durable approach is to express web placement as queries against the master taxonomy plus attributes. On a $2B pet ecommerce catalog I wrote these as Solr queries: a product qualified for a web node if it matched a set of taxonomy and attribute conditions, so a new SKU landed in the right places the moment its data was complete. The business rule lived in the query, in one place, reviewable.

Rule of thumb. If adding one SKU requires a human to decide where it shows on the site, the rules are incomplete. Placement should be a consequence of the data, and exceptions should be rare enough to be visible.

Two consequences follow. First, data completeness becomes the gate for merchandising, which gives the catalog team real leverage to demand attribute coverage. Second, a bad rule is fixable in one edit instead of thousands of rows, so the structure can be revised as the assortment changes.

How to tell yours are merged

Your category tree contains nodes like “Gifts under $50”, “New Arrivals” or “Summer Shop” alongside real product classes.
Required attributes differ between two products that a merchant would consider the same type of thing.
A site redesign forces a data migration.
Finance maintains a private spreadsheet that re-maps your categories before reporting.
Nobody can answer “how many SKUs do we have in this category” without qualifying which category system they mean.

Any one of these is survivable. Three or more means the setup structure and the customer structure are the same tree, and every future change to one will damage the other.

Separating them without a re-platform

You do not need a new PIM to fix this, and re-platforming to fix it usually reproduces the problem in a new system. The sequence that works:

Freeze the existing tree and label every node honestly as product class, marketing construct or reporting rollup. This takes a week and is uncomfortable.
Extract the product classes into a clean master taxonomy. Aim for nodes defined by what a thing is, never by who buys it or when it is on sale.
Define the required attribute set per master node. This is where the real work is, and it is also where the coverage audit tells you what you are missing.
Rebuild the marketing constructs as rules over the master taxonomy and attributes rather than as nodes.
Keep the reporting rollup as a separate mapping owned by finance, refreshed on their calendar, not yours.

Done in that order, the site keeps working throughout, because the navigation is being rebuilt as a view rather than being migrated.