  This note is about the smash product of pointed topological spaces, without
relying on some convenient subcategory. We deal with its partial associativity
properties and their connection with the function spaces, introducing a
property of regular associativity related to the colax monoidal structure of
the product. We also study a large class of triples of pointed spaces where
associativity fails.
  Lax and colax monoidal structures are unusual and interesting, in category
theory. Some parts of this note will be obvious to a topologist and others to a
categorist, in order to take into account both backgrounds.
