Exponentiability in categories of lax algebras. (Dedicated to Nico Pumplün on the occasion of his seventieth birthday).
Exponentiability in homotopy slices of TOP and pseudo-slices of CAT.
Exponentiability in lax slices of .
Exponentiable embeddings in totally reflective subcategories of
Exponential laws for topological categories, groupoids and groups, and mapping spaces of colimits
Exponential Objects
In the first part of this article we formalize the concepts of terminal and initial object, categorical product [4] and natural transformation within a free-object category [1]. In particular, we show that this definition of natural transformation is equivalent to the standard definition [13]. Then we introduce the exponential object using its universal property and we show the isomorphism between the exponential object of categories and the functor category [12].
Extensionable topological hulls and topological universe hulls inside the category of pseudotopological spaces
Extensional subobjects in categories of -fuzzy sets
Two categories and of fuzzy sets over an -algebra are investigated. Full subcategories of these categories are introduced consisting of objects , , where is a subset of all extensional subobjects of an object . It is proved that all these subcategories are quasi-reflective subcategories in the corresponding categories.
Extensions of factorization systems
Extensions of functors and their applications
Extensions of Polylinear Mappings
Extremal subobjects of complete posets