We give sufficient conditions for the existence of a model structure on operads in an arbitrary symmetric monoidal model category. General invariance properties for homotopy algebras over operads are deduced. Mathematics Subject Classification (2000). Primary 18D50; Secondary 18G55, 55U35.

Let N = (R,+, ·, <, . . . ) be an o-minimal expansion of the standard structure of a real closed field R. In this paper, we consider an obstruction theory in the definable category of N . 2010 Mathematics Subject Classification. 55N20, 03C64.

We present explicit examples finite tensor categories that are C2-graded extensions of the corepresentation category of certain finite-dimensional non-semisimple Hopf algebras. Mathematics Subject Classification (2010): 18D10, 16W30, 19D23.

The notion of an internal category in a left exact cosimplicial category is introduced. For any topos over sets a certain left exact cosimplicial category is constructed functorially and the category of internal categories in it is investigated. The notion of a fundamental group is defined for toposes admitting the notion of “a discrete category.” Introduction Our primary interest in this paper...

In this paper we show that to a unital associative algebra object (resp. co-unital coassociative co-algebra object) of any abelian monoidal category (C,⊗) endowed with a symmetric 2-trace, i.e. an F ∈ Fun(C,Vec) satisfying some natural trace-like conditions, one can attach a cyclic (resp. cocyclic) module, and therefore speak of the (co)cyclic homology of the (co)algebra “with coefficients in F...

We describe a sequent calculus μLJ with primitives for inductive and co-inductive datatypes and equip it with reduction rules allowing a sound translation of Gödel’s system T. We introduce the notion of a μ-closed category, relying on a uniform interpretation of open μLJ formulas as strong functors. We show that any μ-closed category is a sound model for μLJ . We then turn to the construction o...

Three experiments showed that the pattern of interference of single-modality Stroop tests also exists cross-modally. Distractors and targets were either pictures or auditory words. In a naming task (Experiment 1), word distractors from the same semantic category as picture targets interfered with picture naming more than did semantically unrelated distractors; the semantic category of picture d...

Motivated by a model for syntactic control of interference, we introduce a general categorical concept of bireeectivity. Bireeective subcategories of a category A are subcategories with left and right adjoint equal, subject to a coherence condition. We characterize them in terms of split-idempotent natural transformations on id A. In the special case that A is a presheaf category, we characteri...