T: n 1955 Buchsbaum showred thet an additive category in which exact sequences behave
reasoniby, enjoys many of the same proporties as the category of abelian groups [1] and [2] …

A pressing problem confronting category theory is that of providing an adequate, precise,
and flexible foundation. Two approaches are currently in use; neither is really satisfactory …

In their paper on a" General theory of natural equivalences" Eilenberg and MacLane laid the
foundation of the theory of categories and functors in 1945. It took about ten years before the …

1. Introduction. Category, functor, and natural transformation of functors are notions of great
generality—and consequent simplicity. They apply to many different parts of mathematics …

These notes contain an account of seminar lectures given at the Mathematical Research
Institute of the ETH in February 1966, an embryonic version having been presented in a …

XXA A X---).(AxX)) Y will be called the" X-transform" of the morphism f. A morphism h: X" yA
is the X-transform of f iff the diagram is commutative, showing in particular that f can be …

It is well known (d. Kan [. § . J, Lawvere CO) that a functor Sets f: induced by cornposition
with---., possesses both a left and a right adjoint provided that the category be sma. ll …

This paper is an attempt to modify set theory in such a way as to provide for the existence of
objects (like the category of groups) indispensable in modern mathematics. Guided by the …

Our purpose is to describe some examples and to suggest some directions for the study of
categories with equational structure. To equip a category A with such a structure means …

Introduction. The taproot of the general (or free-form) functorial semantics of this paper is the
observation that an adjoint connection between two categories is normally induced by an" …