A second category set with only first category functions

Set Theory for Category Theory

Questions of set-theoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made can have noticeable effects on what categorical constructions are permissible. In this expository paper we summarize and compare a number of such “set-theore...

Category of Polygroup Objects

A big symmetric planar set with small category projections

We show that under appropriate set theoretic assumptions (which follow from Martin’s axiom and the continuum hypothesis) there exists a nowhere meager set A ⊂ R such that (i) for each continuous nowhere constant function f : R → R the set {c ∈ R : π[(f + c) ∩ (A×A)] is not meager} is meager, and (ii) the set {c ∈ R : (f + c) ∩ (A × A) = ∅} is nowhere meager for each continuous function f : R → ...

Category of $H$-groups

‎This paper develops a basic theory of $H$-groups‎. ‎We‎ ‎introduce a special quotient of $H$-groups and‎ ‎extend some algebraic constructions of topological groups to the category‎ ‎of H-groups and H-maps and then present a functor from this category to the category of quasitopological groups‎.

Category restructuring during second-language speech acquisition.

This study examined the production of English /b/ and the perception of short-lag English /b d g/ tokens by four groups of bilinguals who differed according to their age of arrival (AOA) in Canada from Italy and amount of self-reported native language (L1) use. A clear difference emerged between early bilinguals (mean AOA= 8 years) and late bilinguals (mean AOA= 20 years). The late bilinguals s...