For 10 points, name this operation with cross and dot forms.
In category theory, pullbacks are the fiber type of this operation. Performing it on an empty family will give a terminal object. Modding out the tensor algebra by the ideal generated by every vector tensor itself gives a space whose elements are formed by the exterior type of this operation. This word names a topology that preserves compactness by (*) Tychonoff's theorem. For two groups, the direct sum is isomorphic to the direct type of this operation, where the elements are ordered pairs of elements in each group and so the underlying set is given by its Cartesian form. One variety of it can be used to find the volume of parallelpipeds or construct normal vectors and another gives the projection of a vector. For 10 points, name this operation with cross and dot forms.
In category theory, pullbacks are the fiber type of this operation.
product