Questions tagged [algebraic-theory]

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7
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0answers
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Michel Thiébaud's thesis (“Self-Dual Structure-Semantics and Algebraic Categories”)

I am looking for a copy of Michel Thiébaud's 1971 thesis Self-Dual Structure-Semantics and Algebraic Categories, which appears to be an early reference for the relationship between the Kleisli ...
8
votes
1answer
185 views

Internal logic of locally strongly finitely presentable categories

There is a duality between locally strongly finitely presentable categories and (Cauchy complete) cartesian categories, i.e. multisorted algebraic theories. The internal logic of cartesian categories ...
5
votes
0answers
94 views

Characterisation of essentially algebraic theories with a fixed set of sorts

It is well known (e.g. Palmgren–Vickers's Partial Horn logic and cartesian categories) that many-sorted essentially algebraic theories (equivalently partial Horn theories / quasi-equational theories / ...
3
votes
1answer
79 views

Characterisation of presentations for varietal large equational theories

Let $T : \mathbf{Set}^\mathrm{op} \to \mathscr T$ be a large equational theory (i.e. a bijective-on-objects product-preserving functor). Following Linton in Some Aspects of Equational Categories, we ...
7
votes
1answer
280 views

Characterisation of essentially algebraic theories as monads

The following correspondence between algebraic theories and monads on $\mathbf{Set}$ is well-known (see, for example, Algebraic Theories: A Categorical Introduction to General Algebra). The ...
4
votes
1answer
321 views

Question about an implication of Thomason's étale descent spectral sequence

On page 5 of this paper by Dwyer and Mitchell, it is said that Thomason's étale descent spectral sequence from his paper Algebraic K-theory and étale cohomology, which reads $$H^p_{\acute{e}t}(X, \...
11
votes
3answers
570 views

IBN for algebraic theories

Let us say that a finitary algebraic theory $\tau$ has IBN (invariant basis number) if the free functor $F : \mathsf{Set} \to \mathsf{Mod}(\tau)$ reflects the isomorphism relation: If $S,T$ are sets ...
5
votes
0answers
306 views

The graph of algebraic theories

Fix a logic $L$ and consider the category $\mathbf{AlgTh}_L$ with theories of $L$ as objects and theory interpretations as morphisms. For nice enough logics, this category has pushouts (which we will ...
5
votes
1answer
449 views

Request for reference: Banach-type spaces as algebraic theories.

Sparked by Yemon Choi's answer to Is the category of Banach spaces with contractions an algebraic theory? I've just spent a merry time reading and doing a bit of reference chasing. Imagine my delight ...