It is shown that the dual algebra functor from coalgebras to algebras has a left adjoint even if the base ring is not a field but an arbitrary commutative ring with 1. This result is proved as a corollary to a more general theorem on adjunctions between comonoids and monoids over suitable symmetric monoidal categories. MSC 2000: Primary 16B50, Secondary 18A40

This article attempts to develop a usable framework for doing category theory in Isabelle/HOL. Our point of view, which to some extent differs from that of the previous AFP articles on the subject, is to try to explore how category theory can be done efficaciously within HOL, rather than trying to match exactly the way things are done using a traditional approach. To this end, we define the not...

We study Hopf and Lie algebras in entropic semi-additive varieties with an emphasis on adjunctions related to the enveloping monoid functor and the primitive element functor. These investigations are in part based on the concept of the abelian core of a semi-additive variety and its monoidal structure in case the variety is entropic. MSC 2010: Primary 08B99, Secondary 16T05

This development proves Yoneda's lemma and aims to be readable by humans. It only defines what is needed for the lemma: categories, func-tors and natural transformations. Limits, adjunctions and other important concepts are not included. There is no explanation or discussion in this document. See [O'K04] for this and a survey of category theory formalisations.

We introduce a new categorical framework for studying derived functors, and in particular for comparing composites of left and right derived functors. Our central observation is that model categories are the objects of a double category whose vertical and horizontal arrows are left and right Quillen functors, respectively, and that passage to derived functors is functorial at the level of this ...