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presheaf
This term is a highly specialized technical noun used exclusively within the domains of category theory, algebraic geometry, and topology. It describes a mathematical structure that assigns data to open sets of a topological space without requiring the "gluing" property that defines a full sheaf. Consequently, it serves as the foundational building block from which sheaves are constructed.
In a mathematical context, the term is treated as a standard countable noun. While it describes an abstract functorial mapping, it is referred to as a discrete object of study, allowing for the discussion of multiple distinct presheaves on a single space.
Ý nghĩa
In category theory and algebraic geometry, a functor from the opposite category of a topological space (or more generally, a category) to the category of sets, abelian groups, or rings, which assigns data to each open set.
The presheaf of continuous real-valued functions on a space X assigns to each open set U the set of all continuous functions from U to R.