Topological half-exact functor

In the context of category theory and algebraic topology, a topological half-exact functor is a type of functor that reflects certain properties related to homotopy and convergence, particularly in the context of topological spaces, simplicial sets, or other similar structures. While the term "topological half-exact functor" is not widely standardized or commonly used in the literature, it's likely referring to concepts related to exactness in categorical contexts.