  This paper introduces Gm, which is a category for extensive-form games. It
also provides some applications.
  The category's objects are games, which are understood to be sets of nodes
which have been endowed with edges, information sets, actions, players, and
utility functions. Its arrows are functions from source nodes to target nodes
that preserve the additional structure. For instance, a game's information-set
collection is newly regarded as a topological basis for the game's
decision-node set, and thus a morphism's continuity serves to preserve
information sets. Given these definitions, a game monomorphism is characterized
by the property of not mapping two source runs (plays) to the same target run.
Further, a game isomorphism is characterized as a bijection whose restriction
to decision nodes is a homeomorphism, whose induced player transformation is
injective, and which strictly preserves the ordinal content of the utility
functions.
  The category is then applied to some game-theoretic concepts beyond the
definition of a game. A Selten subgame is characterized as a special kind of
categorical subgame, and game isomorphisms are shown to preserve strategy sets,
Nash equilibria, Selten subgames, subgame-perfect equilibria,
perfect-information, and no-absentmindedness. Further, it is shown that the
full subcategory for distinguished-action sequence games is essentially wide in
the category of all games, and that the full subcategory of action-set games is
essentially wide in the full subcategory for games with no-absentmindedness.
