Prerequisites: Algebraic General Topology.
For funcoids there are several nicely defined products, including cross-composition product. There is also an attempt to define displaced product.
Cross-composition product is overally nice, but product of funcoids corresponding to topological space is not generally the funcoid corresponding to (Tychonoff) product topology, by the simple reason that cross-composition product of funcoids is not necessarily a funcoid (it is a pointfree funcoid).
Displaced product is deined simply as the displacement of cross-composition product.
For displaced product it is currently not known whether it coincides with Tychonoff product for topological spaces,
It is even not known for displaced product whether product factors can be restored from the product (provided that the product is a product of non-empty factors).
There are also other products of funcoids (reindexation product, ordinated product). Bu these are not pointfree funcoids when the product factors are funcoids, what makes these products possibly less interesting than cross-composition products and displaced products.