This paper examines coherence for certain monoidal categories using techniques coming from the proof theory of linear logic, in particular making heavy use of the graphical techniques of proof nets.… (More)

173. The comments added \in proof" in that paper are incorporated into the body of the text in this version. Abstract There are many situations in logic, theoretical computer science, and category… (More)

0. Introduction. I t is well known that for much of the mathematics of topos theory, it is in fact sufficient to use a category C whose slice categories C/A are cartesian closed. In such a category,… (More)

In the late sixties F. W. LAWVERE showed that the logical connectives and quantifiers were examples of the categorical notion of adjointness. In [9] and [lo] he amplified this notion by a more… (More)

This note applies techniques we have developed to study coherence in monoidal categories with two tensors, corresponding to the tensor–par fragment of linear logic, to several new situations,… (More)

In this paper we describe a deductive system for categories with finite products and coproducts, prove decidability of equality of morphisms via cut elimination, and prove a “Whitman theorem” for the… (More)

Cartesian differential categories were introduced to provide an abstract axiomatization of categories of differentiable functions. The fundamental example is the category whose objects are Euclidean… (More)

Linear bicategories are a generalization of ordinary bicategories in which there are two horizontal (1-cell) compositions corresponding to the “tensor” and “par” of linear logic. Benabou’s notion of… (More)

We show that any free ∗-autonomous category is equivalent (in a strict sense) to a free ∗-autonomous category in which the double-involution (−)∗∗ is the identity functor and the canonical… (More)