… trivial internal categories in the category C of groups with operations satisfying certain …
H(C, -) = 0 iff C is a connected internal category; if 12 = Ab. H 1 (C, -) = 0 iff C is equivalent to …

… In [6] Brown and Spencer noted that internal categories within the category of groups are …
of which algebraic categories, C, were such that a similar result held ie internal categories in C …

… We describe morphisms (= internal functors) and … of internal functors and internal category
equivalence. We show that in this case any internal adjunction implies the internal category …

… In section 3, we prove the main result on the construction of free internal categories within
categories of "groups with operations"; in this the important point is not their existence, but the …

… A group-groupoid is a group object in the category of groupoids [8]; equivalently, as is well
known, it is an internal groupoid in the category of groups and, according to [25], it is an internal …

… Now G, being a group, already has an operation which we shall write as x · y. This is … our
internal category we have constructed a group object7 in Cat. Conversely, given a group object, …

… One method of forming internal categories which we have available in~ is as follows: given
a … a group object in the functor category EfUll, ie we can think of it as a group-valued functor. …

… , internal or fibered categories we are challenged to consider the way in which categorical
properties of those structures transform as we pass from one category … of categories within (or …

… The algebraic operations in operads are presented by … Having an internal category, we are
interested in internal … rise to an internal presheaf M ≀ EG over the double category GG ⇒ EG. …

… internal category theory and commutator theory in universal algebra; the so-called Kiss
difference operation also … we use the additive notation for the group structure . This description of …