On Exponentiable Morphisms in Classical Algebra
نویسندگان
چکیده
منابع مشابه
On Exponentiable Morphisms in Classical Algebra
We study exponentiability of homomorphisms in varieties of universal algebras close to classical ones. After describing an “almost folklore” general result, we present a purely algebraic proof of “étale implies exponentiable”, alternative to the topologically motivated proof given in one of our previous papers, in a different context. We prove that only isomorphisms are exponentiable homomorphi...
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Given a map f in the category ω-Cpo of ω-complete posets, exponentiability of f in ω-Cpo easily implies exponentiability of f in the category Pos of posets, while the converse is not true. We find then the extra conditions needed on f exponentiable in Pos to be exponentiable in ω-Cpo, showing the existence of partial products of the two-point ordered set S = {0 < 1} (Theorem 1.8). Using this ch...
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Let I be a set and let A, f be functions. The functor f↾IA yielding a many sorted function indexed by I is defined by: (Def. 1) For every set i such that i ∈ I holds (f↾IA)(i) = f↾A(i). One can prove the following propositions: (1) For every set I and for every many sorted set A indexed by I holds idUnionA↾IA = idA. (2) Let I be a set, A, B be many sorted sets indexed by I, and f , g be functio...
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ژورنال
عنوان ژورنال: Applied Categorical Structures
سال: 2016
ISSN: 0927-2852,1572-9095
DOI: 10.1007/s10485-016-9458-7