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‘This paper describes a family of logics whose categorical semantics is based on functors with structure rather than on categories with structure.’
‘Furthermore, we prove some theorems about the inversion of functor structures.’
‘That is, if we have two categories, one of which has more structure than the other, then we obtain a functor from the first category to the second simply by ‘forgetting’ the extra structure.’
‘This is part of a very broad-reaching theme in algebraic topology in which functors represented and corepresented by various spaces are used in analyzing geometry and topology.’
‘Suffice it to say that adjoint functors pervade mathematics and this pervasiveness is certainly one of the most mysterious fact that category theory reveals about mathematics and probably thinking in general.’
‘One of the reactions that I've seen to the use of the typical set of functors was that the method of combining functors into complex expressions wasn't terribly straightforward.’